The Math Mom's Puzzles

An Impossible Score

2012-01-27T08:28:00.000-05:00

There was a lot of football talk this week in my household, as the New England Patriots advanced on to the Super Bowl. I asked my husband if he can suggest any football puzzle and he recollected the following story.

A number of years ago my husband discovered that our dentist and a long-time friend happens to be friends with Tom Brady's hairdresser, and occasionally gets invited to the Patriots games. From this moment on my husband's teeth showed a suspicious attraction to the dentist's office. One day, after breaking cement of his tooth bridge, he even found himself in the dentist's home kitchen where he bumped into... who else but the Tom Brady's hairdresser himself, who was on his way to the game. Some football talk and a few hours later they all drove by our house to pick up our son for a Patriot's game.
Next morning my husband excitedly described to me the special box seats and how he almost met Giselle, while our son proudly shared with his summer-camp friends how late he stayed up, how tasty the hot dogs of Gillette stadium were and how noisy the football crowd was.

"What was the score?" asked his counselor.
Our son named the score he remembered.
"That's impossible!" answered the counselor.

What could possibly have been our son's answer?

Top image by Not enough megapixels, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday, January 29th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Great Packing Trick

2012-01-20T06:40:00.000-05:00

Holidays are over and right now is about time to pack decorations into the boxes and shelve them somewhere for 11 long months. Assume that you have 40 identical plastic Christmas baubles that you carefully placed into a flat box like the one sketched below (top view). They fit tightly inside this box.

Suddenly you find another bauble from the same set. How to squeeze this bauble into the same box? Box has a height of one bauble, so no layering.

This puzzle is adapted from a Russian-language journal Kvant.
Top image by Chris_J, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday Janury 22nd(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Why things are not as they appear to be?

2012-01-13T09:59:00.000-05:00

You are likely familiar with this sign on the side-view mirrors of some cars: "Objects in the mirror are closer than they appear."

There are so many signs and instructions in the car that you probably avoid wondering about them up until your kids with their natural curiosity ask you: WHY? Let's try to run ahead of this question and figure out this WHY?

Why and how do you think these side-view mirrors distort reality?

Image by Pratheep P S, www.pratheep.com, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday Janury 15th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

A 9-minute steak

2012-01-06T07:41:00.000-05:00

This is a famous tricky puzzle wrapped in a new story.

You are a cook in a restaurant. A regular picky customer orders a steak that should be done in exactly 9 minutes. How can you measure these 9 minutes if the only precise clocks you have are a four minute hourglass, and a seven minute hourglass?

Top image by kamums, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday Janury 8th(EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Run buddy, run.

2011-12-23T02:11:00.001-05:00

My husband has encountered this real-life puzzle last week and we are both looking forward to hearing your suggestions.

He wants to organize a running race at his work. His center consists of different groups. The group that will win the race will be awarded with a significant prize. We need your help defining the winner.

What does it mean for a group to win the race? Here are your guidelines:

Groups can be of different size, but each group should have equal chances to win.
Wide participation should be encouraged (and rewarded) more than running performance.
Running performance should also be taken into account.
The runners that finish first, second and third should add special bonuses to their groups' total result count.

Therefore, in order to rank each group in this race we need some kind of a function that takes into account all of the above requirements, uses participation and run results and produces a number for each group. Group with the largest number would be declared the winner.

Top image by JerryFest, distributed under CCL.

Your thoughts and ideas accepted any time until midnight on Sunday December 25th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

How long is the movie

2011-12-16T07:40:00.001-05:00

It is a tradition in our puzzle marathon to dedicate a special puzzle to anyone who earns 10 puzzle points. This puzzle is for and about our puzzle master, Jerome.

A friend of Jerome's presented him with a DVD of a special movie he burned for his birthday. It may be the never-seen goofy movie from Jerome's wedding or last year's Holiday party where Jerome was Santa. Jerome is riding a subway home and wondering how long this movie is and whether he will squeeze watching it at home before going out to celebrate at the restaurant. On the front of the disk it is written that disk capacity is 120 min, 4.7GB. On the back there is a clear separation circle between the inner "written" part (lighter area) and outer "clean" part (darker area). Jerome looks carefully at his DVD (pictured below) and sees a solution. What is it?

Answer ideas accepted any time until midnight on Sunday December 18th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Pampers vs. Huggies

2011-12-16T07:40:00.000-05:00

It has been 8 long years since we had a baby in the house, and transitioning along with our older kids we had completely forgotten all the baby nuances. One of them is how to avoid diaper changing in the middle of the night. It wakes you up, it wakes the baby up, the transition out from the cuddly warm blanket to the wet wipe on the baby's bare body in a cold room is a torture, it wakes your partner up, as well as the neighbors. Yet, the Huggies diapers that I purchased started to leak after 4 hours, making it impossible not to change in the middle of the night.

Is there any trick? I couldn't remember from my younger kids' days. I emailed my sister-in-law who recently had twins and all she replied was: "ONLY PAMPERS!!!!!"

Could it be so simple? I checked online and saw similar laconic advices everywhere on babies' forums.

I went to the store and bought the recommended brand. Surprisingly they were exactly the same price as Huggies, like no one was in onto the secret. We used it and, true enough, it doesn't seem to leak for 8-9 hours.

I know that more frequent diaper changes during the day is healthier, but for the night - the problem is solved. The question is: assuming that you leave a Pampers diaper on during the day for 4 hours and during the night for 8 hours, how much money you are saving as compared with Huggies diapers that you would replace every 4 hours night and day. Let's compute it as a percentage of a diaper's price or assume that diapers are 3 for a $1.

Top image by dhinivh, distributed under CCL.

Answer ideas accepted any time until midnight on Sunday December 18th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Die Hard because of St. Ives Riddle

2011-12-09T07:56:00.001-05:00

This innocent riddle was a matter of life and death in the movie "Die Hard with a Vengeance" when protagonist had 30 seconds to solve it and then telephone the villain on the number "555 plus the riddle answer" or a bomb would detonate.

As I was going to St Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
Kits, cats, sacks, wives
How many were going to St Ives?

Can you solve it?

Answer ideas accepted any time until midnight on Saturday December 10th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

How Long is This Limousine?

2011-12-02T04:49:00.000-05:00

This year's Veterans Day parade featured a novelty limousine that sadly was filled with only a few remaining veterans. Two kids were trying to estimate the length of this cool limo. But the limo was moving, albeit steadily. One of the boys decided to walk alongside the moving limo from its back to the front in parade's direction. He made 30 steps. Then he turned back and walked alongside the limo in the opposite direction. He made 15 steps. Assuming that each step is 2 feet, can we figure out limo's length?

Image from flickr, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday December 3rd (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

An Obnoxious Puzzle

2011-11-18T04:24:00.000-05:00

I don't like this puzzle but I think it is fair to share it with you because somewhere on your life journey you will meet or hear or read someone challenging you to this. And then - you will impress everyone with the right explanation.

A person said: "Of my two children at least one is a boy."
What is the probability that both are boys?

Image by plushoff, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday November 19th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Are you ready for the 7th grade?

2011-11-10T09:44:00.002-05:00

This puzzle arrived from Kim, our expert puzzle solver. It was on her 7^th grader’s last math test:

Add grouping marks (parentheses and/or absolute value symbols) to the following to make the equation true:

-4 + -8 + 2 * 6 ÷ -6 + 2 + 5 = 2

You are allowed to ask for your kids' help

Answer ideas accepted any time until midnight on Saturday November 12th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Top image by woodleywonderworks, distributed under CCL.

Halloween dilemma: candy or tchotchkes

2011-10-28T06:08:00.001-04:00

Halloween is approaching in a few days and you still have not bought any giveaways. You usually try to be thoughtful and buy candy as well as tchotchkes for those with allergies or strict parents. Last year expecting 300 kids you bought 300 pieces of candy and 300 tcotchkies. You had only 45 candies and 75 tchotchkes left. Indeed 300 trick-o-treaters showed up according to someones count.

What percentage of the trick-o-treaters took both: candy and tchotchkes?
If you expect 400 kids this year, how many of each, candy and tchotchkes, you should buy to not have any left-overs assuming the same percentages of candy-toy preferences as last year?

Image by eszter, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday October 29th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Magical fragrance - how to share

2011-10-21T04:25:00.000-04:00

Fairy god mother granted two of her favorite fairies a bottle of magical fragrance pictured below. She commanded them to split the fragrance equally.

As fairies were in a state of war with each other they were not keen on sharing the fragrance daily. So they decided that one of them will use half of the fragrance and pass over the bottle with the remaining half to the second fairy. The bottle is semitransparent but not symmetrical in either horizontal or vertical direction. How can the second fairy verify whether the amount she gets is indeed half of the original amount? The bottle was completely full to start with. No measuring marks are present on the bottle and fairy doesn't want to pour any drops of the magical liquid out.

Answer ideas accepted any time until midnight on Saturday October 22nd (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Telling time without the glasses

2011-10-14T06:10:00.000-04:00

This new lamp that you bought for your bedroom - it projects the magical lace pattern on the walls and makes you want to fall asleep in the fairyland of your bedroom any time of the day. Yesterday you fell under this spell and took a nap. When you woke up, you quickly glanced at the clock. Without your glasses on both clock handles looked exactly the same size. You guesstimated the time and went back asleep. When you finally put yourself up and managed to get to your appointment you were almost an hour late.

What time might have been on the clock that confused you?

Want something harder - how many times like these are throughout the day when without telling which clock handle is which you can't guesstimate the time?

Top image by Didier Janson, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday October 15th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Dead presidents: spell or coincidence?

2011-10-06T17:20:00.004-04:00

Do you know that three of the presidents of the United States died on the same date, with the date being not just a random date but the most special date for the country - July 4th. John Adams and Thomas Jefferson both died on July 4th of 1826. Five years later, on July 4th 1831, the fifth president, James Monroe, passed away. All three are believed to have died of natural causes.

If you become a special adviser to the president, would you point to the president such an impossible coincidence and advice your president to take the July 4th off and relax avoiding the suspicious spell. Or would you explain such coincidence in some other way?

Top image by JaseMan, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday October 8th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Handshaking at the UN meeting

2011-09-30T03:17:00.000-04:00

A whole lot of people shook hands and a whole lot refused to shake hands with each other at the currently happening UN meeting in NYC. As UN handshaking is not just a handshaking but a political statement, all these handshakes were carefully monitored and accounted for by the special math agent Ilya 011. Where 011 stands for his ranking in this puzzle marathon.

At the end of the meeting Ilya reported that something fishy is going on as the number of people that shook odd number of hands is an odd number and this is impossible. He was right. It turned out that President Obama extended a handshake to Prime Minister Netanyahu but the latter refused it. The rest of the recorded handshakes were mutual.
The question is: how did Ilya knew to suspect the handshaking statistics?

Disclosure: this puzzle celebrates our 10+ puzzle points winner Ilya. The rest of the characters and events in this puzzle are fictional. Any resemblance is purely accidental.

When two people extend hands for a handshake, this counts as one handshake for each of them. At that time two handshakes total are being recorded and added to the total number of handshakes.

Top illustration by Aidan Jones, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday October 1st (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

How many belts and how many husbands?

2011-09-22T16:57:00.000-04:00

Life is a puzzle. It so happens that every week at least one puzzle walks up into this blog. I may find it in the kitchen, my kids may bring it to me from school, a friend may challenge me at dinner; an old book, a stuffed closet, home renovation, news report - anything can inspire a puzzle. This week was busy and not so puzzle-fruitful. Up until I came to the master bedroom today, frustrated and tired, and discovered the following mess:

How many belts do you think there are and (bonus question) how many husbands these belts may belong to? Please explain your reasoning about the belts, do not just post a number.

Why is this math? Because you may use various logical strategies when answering. Because almost every computer science student have had to write an algorithm that will solve a similar problem automatically. Because it is applicable to anything from wire detection and removal in special effects to weapon detection in satellite imagery or chromosome count in genetic tests.

Answer ideas accepted any time until midnight on Saturday September 24th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

Kant's Clock

2011-09-16T01:53:00.001-04:00

A famous old puzzle.

It is said that Immanuel Kant was a bachelor of such regular habits hat the people in his town would adjust their clocks when they saw him strolling past certain landmarks.

One evening Kant was dismayed to discover that his clock had run down. Evidently, his servant had forgotten to wind it. The great philosopher did not reset his hands because his watch was being repaired and he had no way of knowing the correct time. He walked to the home of his friend Schmidt, a merchant who lived a mile or so away, glancing at the clock in Schmidt's hallway as he entered the house.

After visiting Schmidt for several hours Kant left and walked home along the route by which he came. As always he walked with a slow steady gait that had not varied in twenty years. He had no notion how long this trip took. Nevertheless, when Kant entered his house, he immediately set his clock correctly.

How did Kant know the correct time?

Top image by faungg, distributed under the CCL.

Answer ideas accepted any time until midnight on Saturday September 17th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

Life, in Fractions

2011-09-09T01:41:00.001-04:00

Math is old. Diophantus of Alexandria (now Egypt, then under a Greek rule) who lived 18 centuries ago is frequently called the father of algebra or a satan of algebra. He wrote 13 books that he titled "Arithmetica" containing various numerical problems and their solutions. Diophantus was the first Greek mathematician who recognized fractions as numbers. In a tribute to him one of his admirers described his life as a fraction riddle:

Diophantus' youth laster 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later he had a son. The son lived exactly 1/2 as long as his father, and Diophantus died just four years after his son's death. All of this totals the years Diophantus lived.

The question is whether all this info is enough to determine how long Diophantus lived? Prove it!

Top image by freeasfreedom, distributed under the CCL.

Answer ideas accepted any time until midnight on Saturday September 10th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

A Water and Oil Puzzle

2011-09-02T02:06:00.007-04:00

I think we may have had this puzzle in the past. However as this is one of the most popular puzzles all around the world, I decided to discuss it again. With an extra twist.

A wise man told me this week that he loves to observe how in math simple problems and their solutions can be extended to provide answers to a far more complex problems. His example was a famous water and oil puzzle.

Take a jar of water and a jar of oil. Both jar are identical and have the same amounts of liquid. Pour 1 cup of water from the water jar to the oil jar. Now, take 1 cup from the jar containing the mix of water and oil and pour it into the water jar. Do you have more water in the oil jar or oil in the water jar now? Please explain your solution.

Now, imagine you go to the kitchen to cook dinner and your kids discover the oil and water jars. They keep playing with them, taking a bit from one jar and pouring into another, repeating it again and again with various amounts of liquid (using toy cars and Strawberry Shortcake cups as water containers). Miraculously they manage not to spill anything.

When dinner is ready you see that both jars have the same total amount of oily substance. Now, do you have more water in the oil jar or oil in the water jar?

Image by simplyshatterbug, distributed under CCL.

Answer ideas accepted any time until midnight on Saturday September 3rd (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted a valid solution will get a puzzle point.

What's wrong with Messi's pants?

2011-08-21T05:30:00.012-04:00

Shopping for school supplies, our son picked a cool notebook featuring images and autographs of his favorite players from FBC Barcelona. Later at home he noticed a strangely reversed number "10" on the front player's (famous Lionel Messi) pants.

We were all puzzled. Word UNICEF appears correctly printed on all three players' shirts. Numbers 8 and 9 are oriented as expected on the right part of the other two players' pants. What is wrong with Messi's pants?

Answer ideas accepted any time until midnight on Saturday August 27th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who suggested something reasonable will get a puzzle point.

Average Bunk Size

2011-07-14T22:35:00.010-04:00

You are checking out an overnight camp for your kids for next year. On your family visit to the camp you ask 30 randomly encountered kids what is their bunk size and record all the answers. Surprisingly, the answers deviate quite a lot. How can you figure out (approximate) average bunk size from all these numbers?

Image by New York YMCA camp, distributed under CCL.

This is a tricky puzzle and therefore I am giving one whole week for contemplation and answer submission. At the present moment I don't know either how this should be solved but I do know how this should not be solved. So, let's figure it out together. Answer ideas accepted any time until next Friday July 22nd, on our Family Puzzle Marathon. They will be hidden till then and everyone who suggested something reasonable will get a puzzle point.

A Perfect Family Bed

2011-07-07T13:55:00.013-04:00

Over years of parenthood, we tried various night sleeping strategies recommended in parenting books, seminars, by neighbors, friends or guided by simple exhaustion. When my kids were little and would wake up at night we tried walking them back to their beds and sitting with them till they fell asleep. We also tried leaving a welcoming fold-out mattress in our bed for whomever the night would bring in. We tried barking at them to go back to sleep, or read in their beds. We tried letting them squeeze in our bed, which usually resulted in at least one of us going to sleep in their beds.

We learned that in our large king size bed, little kids tend to rotate around their middle like the hour hand of a clock, usually waking up perpendicular relative to where they started. Our firstborn tall kid now rolls 1-2 feet in either direction and also can spread his long limbs perpendicular to his body, hitting our heads or hips. On such nights, happy to cuddle in with these treasures but unable to fall back to sleep I imagine a perfect family bed. One that could potentially fit all of us: with our daughter rotating around her tush and our son free to roll and throw his hands or legs in any direction. What size should be such bed if we are adults of a pretty regular size, rotating kid is around 4 ft and rolling kid is 5 ft with his limbs approximately half of his height?

Image courtesy of the Furman family.

Answers accepted all day long on Friday July 8th and Saturday July 9th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point.

A Roman Puzzle

2011-06-23T22:10:00.006-04:00

One noble Roman dictated a will on his deathbed requesting to split his possessions between his pregnant wife and the unborn child in the following way. If the child is a boy, he should get 2/3 of the total amount, leaving 1/3 to the wife. If the child is a girl, she should get 1/3, leaving 2/3 to the wife. The nobleman died and a few months later his wife gave birth to twins: a boy and a girl. The smartest men and women of the empire were called to resolve the inheritance dispute. One of them - Stevenus Goodmanus - came up with a solution and a proof that it follows the will as closely as possible. What is this solution?

Image by Steven O'Donald, distributed under CCL.

This puzzle celebrates our 20+ puzzle winner, known nowadays as SteveGoodman18.

Answers accepted all day long on Friday June 24th and Saturday June 25th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point.

The magic with any three-digit number

2011-06-16T21:21:00.005-04:00

My daughter's school teacher is showing kids some number mysticism.
She told them to take any 3 digit number, e.g.793.
Scramble its digits, e.g. 397.
Subtract from the larger of these two numbers the smaller one: 793-397=396.
Add the digits of the remaining number, e.g. for a number 396 a sum of digits will be 3+9+6=18.
Then, continue adding digits of the last number you got till the sum is just one digit: 1+8=9.
Surprisingly, no matter what number you start from and how you scramble it, the result is always 9!

The puzzle is why is this happening. And the extra credit question is how to explain this to a 8 year old.

Top image by Hryck, distributed under CCL.

Answers accepted all day long on Friday June 17th and Saturday June 18th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point.

A Better Soap

2011-06-10T10:04:00.006-04:00

In our family's recent stay at a hotel in Maine, we found the following peculiar soaps in our bathroom.

Do you think mice ate the centers of the soaps, or the design is intentional? Does a soap with a hole in it have any advantages over the traditional fully-filled oval-shaped soap? Can you suggest any improvement to this design that can make this soap even more advantageous?

Answers accepted all day long on Friday June 10th and Saturday June 11th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Is There More To More?

2011-06-02T22:00:00.006-04:00

This is a tricky puzzle, yet a trivial one, depending on how you look at it.

You have a container, such as a glass or a bucket. How to fill this container up three times without ever taking anything out of it?

The answer does not include any outside help, evaporation or divine intervention.

Top image by cafemama, distributed under CCL.

Answers accepted all day long on Friday June 3rd and Saturday June 4th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Fake Utensils

2011-05-25T11:42:00.010-04:00

This puzzle celebrates our puzzle solver Annie, who quietly reached over the 10 puzzle mark.

In this puzzle Annie is Manhattan's top private detective and she is being called to Tiffany's jewelry store to help investigate a fraud. Tiffany's manager informs Annie that they sold 10 sets of the Tiffany & Co Silver Utensils yesterday to 10 different people. Each set consisted of 24 pieces, all of them of the same weight. It came to their attention that one of the sets was a fake set that was supposed to be used as a window display. All the utensils in this set weigh 1/10th of the silver utensils. Tiffany's manager wanted to avoid a scandal and notification of all the buyers of a potential fraud. However, she realized that all the buyers should be called back to the store (with their utensil sets) in order to detect and replace the fake set. She asked Annie for the fastest way of detecting which of the 10 sets is the fake one in order to minimize the commotion and suspicion.

Annnie told her: "Reach out to all the 10 buyers and ask them to come to the store with the utensil sets they bought claiming that they forgot a butter knife that should be matched to their specific set. Once I have all the utensils here, all I need is to use your weight scale one time only to detect which set is fraudulent. You will need to present these buyers with 10 butter knives to leave them satisfied."

Do you think Annie was over-confident? How could she avoid weighting each of the utensil sets and use the scale only once to find the fake set?

Answers accepted all day long on Friday May 27th and Saturday May 28th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Mysterious Pattern

2011-05-19T12:08:00.005-04:00

After the April break a mysterious drawing has been discovered on the asphalt behind the school.

Was it an illiterate toddler, an artistic child, an infatuated teenager, or an adult trying to communicate with the aliens? After careful observation, one second grader screamed: "Wait, I see a pattern!"

What is this pattern?
You can submit your word description of the pattern via the comment form below or feel free to email me the snapshots of your drawings.

Thank you to our friend Peter Tze for sharing this nice puzzle.
Answers accepted all day long on Friday May 20th and Saturday May 21st, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

A couple from Florida

2011-05-13T13:44:00.003-04:00

Last weekend I was vacationing on the West Coast of Florida. While it was still rainy and cold in MA, FL was brilliantly blue, hot and shiny. In general for Massachusetts folk, it is a state you are allowed to descend only after retirement. Florida dreams are what keeps us going through over-scheduled routine, stressful work days and frigid winters. When visualizing paradise most of us think of Florida's clean white sand, palm trees and still leisure.

In Florida I met a peculiar couple. His age digits were a reverse of her age digits. They were relaxed and open about their age differences and said that last year he was exactly twice as old as she was. What are their ages?

Image by Fabio, distributed under CCL.

Answers accepted all day long on Friday May 13th and Saturday May 14th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

How to Choose a Man's Shirt

2011-04-28T21:50:00.008-04:00

I saw a comedian a few years ago telling that his mom was so behind in her laundry that she was wearing her wedding dress.

Well, most of us are not us lucky to fit into our wedding outfits way past our wedding year. Take this man. An important occasion demanded him to find this super white Italian shirt bought years ago for his wedding. Size 16. When he bravely tried it on, his wife noted that the collar suffocates him and he needs about 3mm more space everywhere in-between his neck and the collar all around his neck. What size shirts do you think should this man buy now?

Do you know that the shirt size 16 means that a tape wrapped around your neck and two fingers positioned flat upfront will measure 16 inches.

Image by jeremybrooks, distributed under CCL.

Answers accepted all day long on Friday April 29th and Saturday April 30th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

There are two types of drivers

2011-04-21T22:06:00.015-04:00

This puzzle celebrates our master puzzle solver: Bean.

A holiday table conversation at Bean's household this week was prompted by one of the guests getting stuck on the way to the dinner without gas, which led to musing about two types of drivers. There are those who prefer to live on a safe side, possibly because they have nightmarish memories (or nightmarish fantasies) of their car stopping in the worst place and at the worst time. They refill as soon as the gas meter is showing less than half a tank. And there are those drivers, like our expert puzzle solver Bean, who enjoy taking a bit of risk here and there, rationalizing that to get to know this world you need to explore its boundaries. They zip to the gas station only after the tank is 90% empty and the low gas light turns on.

Do you think that by taking some risk this second group of people can save some time and/or money?
Bean was arguing that she can save a few hours per year and enjoy an extra family movie by pushing refills from 40% full tank to 5% full tank. Is she right? Assume a 17 gallon tank that runs empty in exactly a week, and that it takes 7 min to stop at the gas station.

Top image by gypsygen, distributed under CCL.

Answers accepted all day long on Friday April 22nd and Saturday April 23rd, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Chipotle Math

2011-04-13T14:49:00.013-04:00

A friend who is living abroad told us that what he misses most about the US is Chipotle Mexican food. Curiously, we checked out the new branch that recently opened in our neighborhood and quickly became hooked. It seems very simple: tortilla or taco and a few basic but delicious ingredients:

But the combination of flavors, the freshness of ingredients, the spectrum of spiciness that you can choose from, and just the right proportions of everything make it a special comfort meal.

We noticed that there is claim on some of Chipotle paper cups and wrapping paper that "there are 60-some-thousand flavor combinations." 60,000 is quite a large number. Do you think it is really possible with all these ingredients pictured above?

Answers accepted all day long on Friday April 15th and Saturday April 16th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Eight eights that are a thousand

2011-04-07T16:07:00.005-04:00

This is an easy puzzle that you all are welcome to share with your kids and friends:
Put addition signs between the digits 88888888 to get 1000.

Answers accepted all day long on Friday April 8th, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Meet me at Marshalls

2011-03-31T21:02:00.014-04:00

I love high quality discount stores like Marshalls, TJ Max or Filene's Basement. Nothing could beat the joy of finding a treasure for $20-30 without the guilt of overspending. I venture to Marshalls approximately once in two weeks, at a random day and time, spend there around 30 minutes and go home satisfied by my "shopping drug dose".

Slowly I started to realize that around half of the times that I shop there I run into the same mom from my kids' school. We both get slightly embarrassed, assuming that the other must be living there for our encounters to be so frequent. This mom doesn't work there or hang out there, in fact she seems to spend around 30 mins at the store, like I do.

I am wondering whether our high frequency of encounter means that she indeed comes there every day or that her shopping frequency is relatively rare like mine and it just so happens that our in-between-work-and-school shopping cycles and time tables frequently coincide.

Top image by o5com, distributed under CCL.

Answers accepted all day long on Friday April 1st, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Lemonade Stand: a profitable enterprise?

2011-03-24T12:27:00.017-04:00

With the first signs of spring and a T-shirt weather my daughter recollected her dream of placing a lemonade stand on the street. We have never done it before - our weekends are so packed with activities, and I (who grew up in a socialistic environment) am so uncomfortable selling anything to our dear neighbors. But I know that one day or another I have to let her live this simple dream. I am also certain that this could not be a powder-based lemonade that has that distinct chemical taste. We should go for the real thing. The question is: can this whole enterprise be profitable? I doubt that even my super nice neighbors will pay more than a $1.50 for a paper cup with a fresh home-made lemonade.

Here is a simple lemonade recipe I found on the web:

Ingredients
1 cup sugar
1 cup water (for the sugary syrup)
1 cup lemon juice
3 1/2 cups cold water (to dilute)

Assume that the water is free. Lemons are 3 for $1. It looks like we need approximately 5 lemons for 1 cup of lemon juice. Sugar is 2 pounds for $1.50.
9 oz plastic cups are sold 50 for $2.50.

Is it possible to make any profit with this enterprise?

Top image by Conlawprof, distributed under CCL.

Answers accepted all day long on Friday & Saturday, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Beware of the Friendly People

2011-03-10T13:55:00.018-05:00

How friendly are you? Well, in our age it all depends on how many friends you have on Facebook and how many Twitter accounts are pretending to listen to what you are sharing. MediaMetrix company has hired Anne-Marie (one of our winning puzzle-solvers) to help sort out the friendship connections. They told her that statistical studies have shown that the average number of friends that a person has on Facebook is 120. MediaMetrix was asking Anne-Marie to figure out what percentage of the Facebook users have 300 and more friends and therefore fall into a Very Friendly category.

Their idea was to create a special "Beware of Friendly Me" badge that could be sent to all those Very Friendly people for easy identification. Why? Because they do have a lot of power. Their voices and opinions can be heard on Facebook by over 300 readers and then re-shared further and further. Imagine you or your company mistreating one of those people and later seeing yourself being trashed all around the web. With this badge, you will make sure to give every Very Friendly person a VIP attention and they hopefully will share your praise with the world.

Can you help Anne-Marie figure out what percentage of the Facebook users are Very Friendly?

Top image by Dan Taylor, distributed under CCL.

Answers accepted all day long on Friday & Saturday, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

A Truly International Company

2011-03-10T12:31:00.018-05:00

Our great puzzle-solver, Steve Goodman also known as SteveGoodman18 in the business world, was asked by an unnamed company to open a few offices around the world. The goal was to spread customer support all around the globe so that there would be someone answering the phone at any point in time. Each employee should work for no more than 8 hours, 9am-5pm their local time, and it is desirable for the employee who is finishing his/her shift to have at least one hour overlap with the next employee for information sharing purposes. Steve bought a globe and started playing with a few ideas, placing little post-its at the prospective office locations.

He decided that he can't let people work from a boat in the middle of the ocean, but islands may work. He was contemplating whether it is possible at all as so much of the earth is covered by water. Do you think he came up with a solution? If yes, where are these office locations?

Top image by Alfora, distributed under CCL.

Answers accepted all day long on Friday and Saturday, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

A Movie Casting Puzzle

2011-03-10T11:33:00.025-05:00

Let's pretend that our master puzzle solver, KJ, is a famous Hollywood casting agent. In fact, this is precisely why she goes under the name "KJ" - it stands for Killer Jobs.

Recently a new actress contacted KJ asking to be represented by her. KJ was looking at the woman's profile picture and tried to guess how old she is. In a phone interview, she was cautious about directly asking the woman's age, so she started by sharing that she (KJ) is 30 years old and reminisced about 80's music. But the woman was mysterious about her age. The only thing she mentioned was that when she was as old as KJ is now, KJ was twice younger than what she (the woman) is now.

Can you help KJ figure out the actress's age?

Top image by Xurble, distributed under CCL.

Answers accepted all day long on Friday and Saturday, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

A Rare Walking Occasion

2011-03-01T10:39:00.018-05:00

Let's assume that our great puzzle solver Tom is a showbiz pro as he hinted in the Lady Gaga's puzzle. In fact he is so famous and rich that he has a car with a private chauffeur and he rarely walks. Every day he takes a train home from work (let's say Fifth ave, Manhattan), and his train arrives at the station at the same time each day. His chauffeur drives the distance from Tom’s house to the station at a uniform rate, and times his arrival at the station to exactly meet Tom’s train. He picks Tom up and turns around in negligible time, and drives him home from the station.

One day rushing from work for a romantic dinner Tom catches an earlier train, and arrives at the station an hour earlier than usual. He was not able to notify the chauffeur of his early arrival. Trying to get home fast he starts walking home along the route the chauffeur takes, at a brisk rate of 3 miles per hour. When the chauffeur, going to meet the usual train, sees Tom walking, the chauffeur stops, picks up Tom, and quickly turns around. They arrive home 40 minutes earlier than they usually do.

At dinner time, Tom's date is surprised to hear that he actually walked to be ready on time and is curious how long was the distance that he covered by foot. Can you help Tom figure it out?

This puzzle was suggested by Lawrence K. It is featured in a few old math puzzle books.

Top image by Clodius Maximus, distributed under CCL.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

New Kitchen Chairs

2011-02-24T10:11:00.010-05:00

This puzzle celebrates our 20 puzzle point solver - Wang. It goes like this:
Wang and a friend have been shopping for new kitchen chairs. They went to a few stores, tried sitting on the wooden chairs, plastic chairs, aluminum chairs, counter stools and bar stools. To their surprise they found most of the four-legged chairs less stable than most of the three-legged chairs that they sat on. Wang has been contemplating about this all the way home and suddenly it occur ed to him that there is mathematical truth behind their empirical observation. What is it?

Top image by Fernando G., distributed under CCL.

Is Lynnet Misleading Lady Gaga?

2011-02-17T13:23:00.013-05:00

Stefani Germanotta (better known as Lady Gaga) was planning her post Grammy concert in New England. Her newly hired manager, the famous young math whiz named Lynnet did some statistical analysis and told Lady Gaga that in Boston, MA there are about 10,000 fans who are likely to attend her concert even if they need to drive for two hours, in Hartford, CT - 9,000 fans and in Providence, RI - 8,000 fans who are similarly so eager to see Gaga that they could drive almost anywhere in New England. Each of these cities have large concert halls capable to fit audience of up to 30,000. Distance between Boston and Providence is about 50 miles, Boston and Hartford is 100 miles and Hartford and Providence is approx. 80 miles. Lynnet and Lady Gaga met in the office and contemplated where to hold the concert in order to minimize the total amount of miles travelled by all the fans. Lady Gaga concluded: Ok, then Boston it is, as the city with the largest amount of fans. But Lynnet convinced her otherwise. How? And what city the concert is going to be?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Love Triangle

2011-02-10T13:46:00.015-05:00

Dating and Love - what do they have to do with math? This mischievous Valentine's puzzle shows that math may very well be the guiding hand in some romantic adventures.
One man had two lovers. One was a witty, fashionable journalist that lived in the North of the city, and another, passionate and eccentric actress that lived in the South. The man couldn't quite make up his mind about whom he loves more. So every day after work he walked to the Subway, went down the escalator and took the first train that would come. On his right were trains heading North, on his left were trains going South. Whatever train came first determined which lover he would spend the night with. He thought that because the trains go on a regular schedule, with the same frequency in both directions, he would end up spending about the same amount of time with each. He told each of the lovers that on the days he is not with her, he is travelling on a business assignment. All was going well, until one day the journalist confronted him claiming that he has been spending only about 2 days per week with her, while the actress started hinting that he has been crowding her life.

I do not understand, thought man. The trains are regular, I choose randomly, why do I get to one lover much more frequently than another?
What do you think?

Image above is by Nick Sherman distributed under CCL.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Cookies and Milk

2011-02-03T09:15:00.016-05:00

This puzzle comes with a prize! First person to submit a correct solution will get a Mastermind game from the Pressman Toys. To read about the history of the Mastermind game, click here.

The new school principal thought she'd get the children to drink the milk at recess more cheerfully by offering cookies with it. She ordered a box of cookies delivered to school daily. A lot of children had cold and were out on different days. One day the principal noted that if there were five fewer children the next day, each kid would get two more cookies. However, the absentee list was low the next day, and she had four more children instead of five fewer. As a result each child received one cookie less than the day before. How many cookies did the children get the second day?

This puzzle is from the "The Mensa Genius Quiz-a-day book" and every ordinary genius like you can solve it.

Image above is by michelleTNS distributed under CCL.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. Please, explain your answer.

Help Create The Restaurant Menu

2011-01-27T16:09:00.027-05:00

This puzzle is dedicated to our most recent 10-puzzle-points winners: Donna, Dennis, and Katrina.

Katrina and Dennis, who happen to be a husband and wife, decided to lease the popular spot no longer occupied by the Hollywood video and open a restaurant. But what is a restaurant without a top chef? They lured in a rising Food Channel star - chef Donna. Smart and creative as usual, they decided on a restaurant gimmick - college students employees will help your kids do homework while you can enjoy the food, wine and an uninterrupted conversation.

The DDK Family Restaurant has been open for only a year and already got the prestigious Best Afterschool and Less is More awards. The local news channel did a poll of the restaurant visitors and found that 70% had their own single favorite among the 10 amazing dishes Donna created and always came back for it. The remaining 30% percent wished there would be some new entries every time they come - something that Dennis and Katrina didn't offer so far. Dennis and Katrina invited Donna for a brainstorming session to interpret the results of this poll and see how they can make their customers even happier. Donna said that she can not offer more than 10 choices each day. Can you help them figure out how frequently and how many items on the menu they should vary?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point. If you feel some information is missing - make any assumptions you want, just state them specifically.

What's wrong with your head?

2011-01-20T20:55:00.010-05:00

A fun puzzle from my son's friend. Thank you, Elliot!

A man set out for a walk. At the end of his walk his head had travelled 40 feet farther than his feet had travelled. He was a healthy man with all his limbs intact before and after the walk. So how did his head travel farther than his feet?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point.

Image by darkpony. distributed under CCL.

Which One Is Your Carpet?

2011-01-13T21:40:00.004-05:00

Image by vshioshvili, distributed under CCL

Post-Holidays sales are here. You come to a home decoration store and splurge on a new carpet for your living room. When you drive to pick up the carpet at the back of the store, you see 3 different carpet rolls packed for shipping. Which one is yours? They all appear to have exactly the same type of carpet, all tightly rolled, and only vary by the size of the roll (base of the carpet cylinder). Can you figure out the length of the carpet from the diameter of the roll and size of the little empty hole in the center?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point.

New Tires: When Do You Need Them and Tricks You Should or Shouldn't Do With Them

2011-01-06T23:07:00.009-05:00

If on a recent winter family vacation you car was screeching, barking and jumping like a scared small puppy (as our car) instead of smoothly gliding through little hills of the freshly pressed snow, you may need new tires.

We learned that a simple penny test can tell whether tires have been so brushed by use that they lost necessary friction. Ridges on the tire should be at least 1.6mm deep for a safe driving on a slippery surface. This means that if you place a penny in the tire ridges, you should not be able to see the tip of the Abraham Lincolns’ hair on the penny. The expected tire use is 6-10 years. It is usually recommended to replace all 4 tires at once.

Now, a puzzle:
Assume that you just bought four new tires for your car. Your car manual says that your front tires could last you 25,000 miles. Your back tires 15,000 miles. You are trying to be creative and come up with an idea of switching your front tires with your back tires after driving 10,000 miles. What tires will go bad now? When?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something reasonable will get a puzzle point.

Lost Boarding Pass and Your Destiny

2010-12-23T14:29:00.015-05:00

Many of us are traveling this Holiday time, visiting family and friends or running away from them to the mountains or remote islands. Chances are you may be reading this puzzle in the airport. Hold on tightly to your boarding pass.

In this famous puzzle adapted from Peter Winkler's book, we imagine ourselves boarding Aloha airlines airplane from Honolulu to Maui. Everyone is relaxed and happy. The first person that ascends the stairs to the plane holds his boarding pass in in his lips as both of his hands are holding two puppy cages. He smiles to the flight attendant, letting the boarding pass twirl down through the stairs and under the plane. He hesitates for a moment but then decides to perches himself into a random seat. Every next person goes to his or her assigned seat, but those who find their seat occupied politely avoid the argument by taking any random free seat on this short flight. You are the last passenger to board this fully packed 100-passenger plane. The problem is that you pleaded the Aloha ticket counter person to seat you next to this gorgeous surfer and now no longer sure both of you will get your assigned seats. What are the chances?

Image by rantingfan, distributed under CCL

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who contributed something sensible will get a puzzle point.

The Perfect Presents Puzzle

2010-12-16T08:55:00.016-05:00

Image by triplezero, distributed under CCL.

You are going to visit your friend in Chicago for the winter Holidays and emailing her to find out the exact ages of each of her 3 children (all girls) to buy them presents. She is texting you back, but apparently distracted with the fever of her youngest daughter, all she writes is that she wants to talk to you about kindergarten for the next year. She also mentions that last night kids calculated that the product of their ages is equal to her age. You search on Facebook and see that she was born in May 1974. What are you to do about the presents? Is there any way to figure out her kids' ages?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who solved correctly will get a puzzle point.

Chances Of A Random Encounter

2010-12-09T14:12:00.012-05:00

You stop by Starbucks every day after dropping kids at school. You see that you come there randomly between 8 and 9am as sometimes you pause near the school to chat to some other parents, occasionally you go to a CVS first. A few times you run into your boss at Starbucks who is also stopping there between 8 and 9am randomly. You each spend around 10mins standing in line, getting your latte, mixing milk or sugar and zooming off to work. You really do not like these "early morning" encounters that demand a "small talk". You prefer to get caffeinated, clear your mind on the way and slowly transition from the "family" into the "work" mode. You consider switching to a different coffee shop but this one is right on your way. You contemplate: what are the chances of me encountering my boss at this Starbucks location on any given day?

This puzzle is very applicative to other life situations but it is not at all easy. I think we can solve it all together. Everyone who participate will get a puzzle point. First - please submit your individual answers by end of the day on Friday, December 10th. Answers will be hidden till Saturday morning. After the answers are revealed on Saturday, we'll continue brainstorming together.

Last One Is A Rotten Egg

2010-12-02T12:03:00.008-05:00

Real life puzzle today. You buy a dozen eggs, you use them to cook. Noticing that just a few are left, you buy a dozen more. You fill up all the empty egg spots in your refrigerator, then refill and buy more as necessary. How do you make sure that your egg queue is not violated and that those purchased first are being used before those purchased last? That no eggs stays for too long. That the last egg you pick from the corner of your refrigerator's egg tray in not the rotten one.

Ideas accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who shares egg wisdom will get a puzzle point.

Uninvited Thanksgiving Guest

2010-11-25T22:05:00.006-05:00

You have been enjoying Thanksgiving dinner with your family, when the doorbell unexpectedly rings and a young gentleman that appears to be completely lost is inquiring whether Jane by any chance lives in your house. You tell him that you have Janette, Julia and Judith but no Jane, and you ask him how you can help him find this Jane.

He tells you the story of how he met a young Math student named Jane in Cambridge a few weeks ago. They spent a great evening together and then spoke a few times over the phone. Two days ago Jane invited him to join her and her family for the Thanksgiving dinner but she mused that he should figure the address from a puzzle. She told him that she lives on the even side of the long Beacon street. There are six houses on her side of the street in her block, and the sum of their numbers is 9870. She lives in the house with the lowest number among them.

She told him to figure out the number and come around 4pm. It is 6pm now and he was knocking on every first even-numbered doorbell searching for her house.

Do you think you can you help him?

(this puzzle is adapted from the The Mensa Genius Quiz-a-day book by A.F.Salny)
Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who provided a correct solution will get a puzzle point.

First Assignment

2010-11-18T22:16:00.008-05:00

This puzzle is celebrating our master solver Wang who recently turned his 20th puzzle.

Government of Canada (where Wang lives) observed his brilliant puzzle solving skills and hired him to join the Canadian Security Intelligence Service. It is so cold up there that even terrorists are trying their best to avoid this country. So, CSIS is busy monitoring the drug dealers. On his first assignment, Wang has bee sent to arrest a man living in an apartment 4A on the PrairieDog street. Neighbor pointed Wang to the apartment where the man and his wife live and warned that it is hard to tell who is who. Upon entering the apartment, Wang confronted two people. Both had long hair, ruggy clothes and were of unclear gender. "Who is the man in this house?" asked Wang authoritatively.
"I'm a woman," said the person on his left.
"I'm not a woman," said the person on his right.
The super new static lie detector in Wang's pocket beeped signifying that at least someone here is lying. Whom do you think he should arrest?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who provided a correct solution will get a puzzle point.

Should you do this in a car?

2010-11-09T21:46:00.011-05:00

Do you leave home in a rush in the morning and continue your beautification routine in the car? Do you floss, shave, pick your nose, put make-up or lipstick while driving assuming no one around will pay any attention? Well, sometimes... Then, this is a great puzzle for you:

Illustration by Mike Kline, distributed under CCL

If you can see a driver behind you in your car's rear view mirror, does it mean this driver can spy on your beautification routine? Please explain your answer.

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who provided a correct solution will get a puzzle point.

Post-election Party

2010-11-04T12:25:00.007-04:00

Photo from Flickr distributed under CCL

Mid-term elections. 2010. You did it! Yours and others volunteer work and donations placed your candidate at the post. Supercharged with excitement you are celebrating at the post-election victory party. Unfortunately, you are also exhausted and can't locate your watch. When you ask an attractive woman next to you what time it is, she presumes you are drunk. "Let's see if you are capable to drive" she says. "If you stay an hour longer, it will be three time more past midnight than it is now. What time is it now?"

Note: your answer won't be visible untill Saturday morning. Everyone who answers correctly will get a puzzle point. These are new rules of our Family Puzzle Marathon. Solve 5 puzzles and we will send you a prize. Solve 10 and we will write a puzzle about you.

Unguarded Halloween Treats

2010-10-28T14:16:00.006-04:00

Halloween evenings are exciting and busy. Your kids are dressed up way in advance and couldn't wait to start trick-o-treating. As soon as first darkness descends, you finally figure our your costume, and get to the streets to walk your kids from house to house making sure candy goes to the pumpkin and not straight into their mouth. But who will stay at home to give away your candy? You decide to leave the giant bowl of candy outside of your front steps. While trick-o-treating with your kids you noticed that this year there are twice as many little kids as older kids walking around. When you return in an hour, the bowl is empty. You are wondering how quickly all the 350 Kit-Kats have gone and how many kids may have stopped by. You are pretty sure little kids took one candy each as they were supervised by their parents. As for the older kids, you suspect that half of them may have snatched two candies. Can you estimate how many kids stopped by your house?

A Special October?

2010-10-15T21:51:00.004-04:00

This October is very special. It has 5 Fridays, 5 Saturdays and 5
Sundays all in 1 month. This happens once in 823 years. These are known
as money bags. Pass this along to 8 good people and money will appear in
4 days based on the Chinese Feng Shui. Those who stop it will experience
none.

Well,I received this message over 4 days ago and no money appeared so far. I am sending it now to over 1,000 good people and will let you what comes. While we may not be able to predict the fortune, I think we can check whether this October is indeed as special as stated: Is it true that October that has 5 Fridays, 5 Saturdays and 5 Sundays happens only once in 823 years? Seems suspiciously rare

Tom's Surprise Party

2010-10-14T09:42:00.009-04:00

This puzzle celebrates our great puzzle-solver Tom who masterfully cracked 10 different puzzles in our Family Puzzle Marathon.

Image from Flickr, distributed under CCL

Tom has been anticipating his upcoming birthday with a tremble. Do they all remember? What is my family planning to do for me? Will my old college friends show up for this big date?

He was startled when on Monday, a week before his birthday, his wife announced that they are going to have a surprise party for him one day this week.

"How it could be a surprise if I already know about this?"

Master of logical deduction, Tom started reasoning whether and when the party can take place:
"The party cannot happen on Sunday, because if it hasn't happened by Sunday,
I will know it has to happen on Sunday. Then it won't be a surprise."

"The party similarly cannot happen on Saturday, because if it has not happened by Saturday, I will know it has to happen on Saturday or Sunday. We just proved that it can't happen on Sunday, so Saturday it is. But them it can't be a surprise party."

Using the same logic Tom concluded that surprise party cannot happen on Friday, Thursday, Wednesday, Tuesday and Monday and became absolutely convinced that party is not going to take place at all. Is he right?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

This puzzle is adapted from the "Einstein's Riddle" book by J. Strangroom

Math can save lives, admiral!

2010-09-30T23:14:00.006-04:00

During the Second World War, the British Army adopted a naval convoy system for all their merchant ships. Each convoy consisted of 30-70 freight ships and was surrounded by patrolling ships or airplanes. To minimize the chances of convoy being discovered and bombarded by the enemy submarines, the commandment considered two options: sending each convoy as one big flotilla, or splitting the convoy into a few smaller convoys and sending each separately. Can you help the commandment to make this decision?

Naval convoy usually consist of a few merchant ships surrounded by escort ships or airplanes. Looking from the air, we could approximate a convoy as a large blob or circle on the water. What do you think will have higher chances of safely arriving to the destination, one big blob or few small ones?

Playground Safety

2010-06-24T23:30:00.009-04:00

Image by StormyDog

How do you know whether you kid will fit inside the slide or she/he is too tall for it?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Dating Math Puzzle

2010-06-24T23:07:00.010-04:00

Image by BostonBill

On a hot date, young gentleman was trying to guess the age of his new acquaintance. She was flirting and refusing to reveal it. Then he offered her the following game:
He asked her to take the number of the month in which she was born (January - 1, February - 2, etc).
Double it.
Add 4.
Multiply by 50.
Add her age.
Subtract 200.
And tell him the answer.

After that he looked at her very suspiciously and quickly drove her back to her house. Why?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

Airport Games

2010-06-24T19:45:00.011-04:00

Imagine that you are stuck in the Newark Airport because of a silly security breach or thunderstorms and you are going out of your way keeping your kids awake and entertained for a few extra hours. Their favorite thing to do is go back and forth on the moving walkway. Your daughter is daring you to a race. She says: "Let's see who is faster: you going ALONGSIDE the walkway all the way to the end and then coming back, or me going ON the moving walkway first time in the direction of the motion and then back, against the direction of the motion. I will try to keep the same speed both ways." You are tired and frustrated because of the delay, but you are a parent. So, you agree. Who do you think is going to win?

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

How Long is the Traffic Jam?

2010-06-18T09:07:00.008-04:00

Image from Flickr

There was a giant traffic jam on I-95 yesterday. It seemed that 3 out of 6 lanes were closed and on the remaining lanes cars were driving with half the regular speed. Freeway was packed during the rush hours and people said that traffic jam continued for a few miles North. I am wondering whether someone has any suggestions on how to help police (and drivers) estimate the expected size of the traffic jam if they need to close half of a freeway in such a manner. What will happen if they close one lane? Two lanes? You can use your kids' computer games, real life examples, internet and real police help in your answers.

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Best Document Review Strategy

2010-06-18T08:46:00.010-04:00

Life is a Puzzle. Right? You just need to stop and think: "Why am I doing this?" to come up with some creative ideas on why you should not do this or how to do it better. Otherwise, you'll just continue being a tiny little piece of this 1000+ piece puzzle.

Many of us frequently need to review some documents at work. Assume that a new product manual is being published and five people need to review and approve every word. Technical writer usually creates such document and sends it for review to all five people. Each one of these people returns comments to the writer. Writer incorporates all the comments and sends for another review. What if someone has a comment on someone else's comment? This can go on and on till no more new comments are sent and everyone agrees with every word of the document. This approach doesn't take long as everyone comments in parallel but it requires many repeated reviews. And you know how everyone becomes less and less vigilant with every next review. Can you offer an alternative approach: easier, faster or perhaps more stimulating or rewarding? How you solve this real life puzzle in your work? Creative ideas are specially encouraged.

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Just a Walk Around the Block

2010-06-18T08:07:00.008-04:00

Image from Flickr

You go for a walk around the block with your daughter and. Two-thirds of the way, she stumbles, falls and gets a booboo. "Mommy, I have blood!" Some tears, some sobbing, some thumb sucking. You give your daughter a piggy-back ride the rest of the way and spend twice as much time on this little interval as you did while walking together. Father sees you approaching your home and says: "Hey, it looks like stuck on top of each other you are twice slower than walking side-by-side. I wonder how fast we'll go if I take both of you on my shoulders?" Is his estimation correct?

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Mathematician in the Law School

2010-06-10T22:34:00.022-04:00

Our most celebrated puzzle-solver, Kim the Ingenious, decided to attend a prestigious law school. With her sharp mind, clear logic and great persuasion abilities, she managed to convince the Law School administration to sign up for a deal. This deal would contractually oblige Kim to pay double the school fees, but only when she wins her first case. Until then, she would be required to pay nothing.
However, what Law School administration did not know was that Kim only ever intended to take on cases that she could not possibly win. As soon as she entered the Bar, she chose only those clients who have committed their crimes live on national TV and then sighed a confession in front of millions of people.

Unfortunately for Kim, the new dean of the Law School she attended, Prof Protagoras, was not prepared to tolerate her shenanigans any longer. The Professor came up with a plan every bit as devious as Kim's. He decided to sue Kim in court for the money she owes.

Professor does not expect the law school to win the case, but he believes that it will end up getting its money anyway. He reasons as follows: if Kim wins, then she will won her first case, which means she will be obliged to pay the amount she owes. If she doesn't win, then it means court has confirmed that she has to pay the money. Either way, Law School gets paid.

Needless to say, Kim does not see it quite like this. She believes that if she wins the case, it means the court has determined that she doesn't need to pay the money. If she loses, she has still not won her first case, which means that she is not obliged to pay. So, either way, the law school does not get paid.

Which of the two of them has got it right? And why?
This intriguing puzzle was adapted from a great book by J. Stangroom "Einstein's riddle."

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Bullfight in Barcelona

2010-06-10T22:34:00.021-04:00

This puzzle is rated PG-13 and touches a controversial issue.
We all heard about the Spanish tradition of bull fighting and have suspected it is still being practiced somewhere around the globe. Have you ever assumed you would witness one yourself?
Walking around Barcelona, my husband and I came to an intriguing castle that turned out to be Plaza de Toros Monumental, a bull fighting arena. We were fascinated to learn that it so happens that a rare bull fighting show is being held on the evening of the same day. Now, we strictly oppose animal cruelty. I stopped buying any leather or fur coats many years ago. My husband attempted vegetarianism but eventually we put a line at eating meat only once a week. Still, watching Corrida - Spanish bull fighting show - looked like once-in-a-lifetime-experience. It would happen with or without us. So, perhaps it is worth experiencing it. We bought the tickets, changed our plans and ambivalent about our actions, arrived to Plaza De Toros at 7.30pm.
It was a show: well-staged, acted, but disgusting and morally terrifying. In an hour during which our curiosity overstretched our guts, we saw four bulls masterfully killed right in front of our eyes. One was given a "parole" by the cheering crowd and the Presidente who looked like Don Corleone presiding over the show. I assume that at least two more bulls were killed after we left before the show was over. Six total.
I won't share the barbaric details of the process. It seems like this tradition is going away in Catalonia and perhaps in the rest of Spain. By observing it once most will alter their perception of Carmen's toreador and remove the imaginary veil of romanticism and heroism from bull fighting.
Apparently half of the meat from the killed bulls is donated to the poor and the rest is being sold to the restaurants around the town. Among the guilty nightmarish thoughts that occurred to me after the show was: what are the chances that we'll be eating meat from one of these six bulls served for dinner tomorrow? According to a recent survey, there are around 11,000 restaurants, bars and cafes in Barcelona. Say, each bull weights around 1,000 pounds. Assume that each meat portion is around half a pound. Dare to answer?

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The best deal on a plane ticket

2010-06-10T21:42:00.009-04:00

Summer is a time of vacations and many of us have been or will be purchasing plane tickets for these long-dreamed-about trips. I usually look for a minimum number of stops, convenient hours, not too short and not too long a layover, and a familiar airline. Then, I go for the cheapest selection on this list. The difference between the least expensive choice and the next one is usually around 5%. That can be $50 for an International flight or $15 for domestic. Sounds like a good strategy, right? On my recent trip I was not so sure about that.
My least expensive choice didn't have personal TV screens in front of every seat, something that became very common on large planes and long international flights. On the way back, audio, light and even flight attendant buttons didn't work for the whole row of seats I was in. Toilets were dirty, food bad, flight attendants not very courteous. There were no eye cover and comfy socks that I know are being offered (or have been a year ago) on the airline that was next in price. Long-distance flights are never easy but for parents-flying-solo they can be rejuvenating: read, eat, watch, chat and sleep. Just yourself to worry about for a few hours or perhaps even a whole day. Quantifying all the things I expected by didn't get on my last trip, I am wondering whether this $50 difference was significant.

Perhaps I should adopt the same strategy as in a restaurant wine selection rule: pick second from the least expensive and you won't miss. What do you think?

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The Thieving Clown

2010-06-04T08:59:00.006-04:00

The trainee clowns at Bozo College are in a state of shock. A thief has deprived the college of 873 yellow balloons and a broken-down balloon pump. Happily, there was a witness to the crime, who was stated that the thief was wearing the College's clown uniform and had a red nose. Previous research has shown that on 80 percent of occasions witnesses will correctly identify the color of the nose of a clown involved in committing a crime. It is also known that 85 percent of the clowns at Bozo College have blue noses and that 15 percent have red noses. What is the probability that the thief had a red nose (assuming that the witness it telling the truth about what he thinks he saw)?

This puzzle is from the great new book by J. Stangroom "Einstein's riddle" that is listed on our Math Resources page.

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The Case of the Arctic Hero

2010-06-04T08:44:00.008-04:00

Young man has been trying to impress his dancing partner at the high school prom. He told her about his father who participated in the Arctic Expedition. One winter day his father found himself on a piece of ice that broke loose and was drifting out to sea. He quickly realized that he and the his dogs would freeze out to death unless he started a fire. Alas, he had used up all of his matches. So, he got out a small magnifying glass from his instrument kit and, tearing off sheets from his Arctic Guide book, laid them on a steel instrument box. By focusing the sun's rays through the glass onto the paper, he started a hearty blaze. Fortunately, an ice cutter picked him and the dogs up after 24 hours. Young man was obviously very proud of his father, but the girl - his dancing partner - was rather suspicious. Why?

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This great puzzle is one of the Two-Minute Mysteries from D. J. Sobol book.

Enormous Lot

2010-06-04T08:30:00.005-04:00

Over drinks in Vegas one Real Estate developer has been boasting about an enormous piece of land he got in Montana. According to the developer his land was in the shape of a triangle. One side of the triangle reached 200 miles from end to end. On each of the other two sides lot extended 100 miles from corner to corner. All of the listeners were impressed except for one. That woman merely laughed and said, "Why a lot of that size wouldn't even have to pay taxes where I come from."
Strangely enough, this woman was correct. How could this be so?

This puzzle is adapted from a book "Puzzle it out" by E. Richard & L. Churchill.

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Metal Water Bottlle in the Dishwasher?

2010-05-28T10:12:00.007-04:00

Someone in my household put a long metal water bottle in the dishwasher. Let's simplify and assume that this water bottle is just a 10" long and 2" diameter cylinder. Disregard that the top part is narrower than the rest.

I am wondering what are the chances that throughout the dishwasher cycle at least one water drop will reach bottle's bottom from the inside? Assume that we had a sweet lemonade in the bottle before and really need this stickiness washed. Any thoughts are accepted. We don't exactly know from where dishwasher shoots water, so assume random directions.

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Easy Money

2010-05-28T09:59:00.004-04:00

Years ago a blacksmith put a set of new shoes on a horse owned by a wealthy but stingy rancher. When the job was completed, the blacksmith charged the rancher ten dollars for the job. The rancher claimed the price was too high and refused to pay.
"Very well," the blacksmith told him, "I'll make a deal with you. Each horseshoe has eight nails. There are four shoes on the horse. Four eights are thirty-two. I'll charge you one cent for the first nail, two for the next, four cents for the next, and so on for all thirty-two nails."
The rancher agreed at once and reached for his wallet. How much will he have to pay?

This puzzle is from "Puzzle it out" book by Richard and Churchill.

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Two Miners - a tribute to M.Gardner

2010-05-24T14:35:00.001-04:00

These two miners come out from a coal mine at the end of their working day. One of them has his face covered in soot and the other one still has a perfectly clean face. They both glance at each other in the elevator bringing them back to the surface. When they get home, the one with the clean face cleanses himself thoroughly and the other one does not. Why?

This puzzle is from the Martin Gardner's "Aha!" book.
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Guess My Phone Number - a tribute to M.Gardner

2010-05-24T14:27:00.004-04:00

Try to guess my phone number (10 digits). You can ask me 20 questions and I will answer by Yes or No. How can you do that?
This puzzle is from the Martin Gardner's "Aha!" book.

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How long is the Loch Ness monster? - a tribute to M.Gardner

2010-05-24T14:24:00.005-04:00

The Loch Ness monster's length is 20 meters plus half of its length. What is his total length?

This puzzle is from the Martin Gardner's "Aha!" book.
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How long did he live?

2010-05-21T08:13:00.006-04:00

Here is an ancient Greek puzzle about Diophantus, who is believed to be the father of algebra:
This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.

How long did Diophantus live?
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Doctor's Dilemma

2010-05-20T20:54:00.010-04:00

Three sisters - Hannah, Hope and Hillary - are identical triplets. However, while Hannah always tells the truth, Hope always lies, and Hillary is only occasionally truthful.

All three sisters came to the doctor's office but only Hope needed to get her influenza shots. Confused to see three identical faces, doctor asked the sister that was sitting on the left, "Which sister is in the middle of you three?" and the answer he received was, "Oh, that's Hannah."
Then he asked the sister in the middle, "What is your name?" The response given was, "I'm Hillary." Confused, he turned to the sister on the right, then asked, "Who is that in the middle?" The sister then replied, "She is Hope."

Frustrated to receive three different answers to the same question, doctor turned to logic. Can it help him figure out which sister to take for the shot?

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A Chain Loan

2010-05-20T17:14:00.011-04:00

Greek Government recently got a $140 billion aid package from the International Monetary Fund. Imagine that International Monetary Fund would like to get some symbolic collateral for the loan and is eying an ancient gold link chain (believed to belong to Aphrodite) from the Athens's Museum. The chain has only seven links, all connected in a row. Monetary Fund wants one link for each year until the loan is returned. Meaning that it wants to hold to one ring in the first year of the loan, two rings in the second, three in the third etc. Greek government agrees but demands that chain be minimally damaged and only one link out of the whole chain be cut. Is that possible?

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A Working Holiday

2010-05-20T14:21:00.008-04:00

This may have happened to you. Take Veterans Day, Martin Luther King Day, Presidents Day - or any other holiday observed by your child's day care but not observed by most of the private companies. If both, you and your spouse, work and you have not arranged for a babysitting, you are facing a puzzling day. Could you manage? Assume that your child sleeps 10 hours at night and naps 2 hours during the day. You and your spouse each need 8 hours of sleep in order to function responsibly. Is it possible for you to split the day so that both, you and your spouse, will each squeeze a full 8 hour working day and split childcare?

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Sam Loyd's Cashier Puzzle

2010-05-14T09:24:00.003-04:00

This puzzle comes from one of the greatest puzzle makers, Sam Loyd, who lived over 100 years ago. It tells of an old man who stepped into a bank with a check for $200 and asked the cashier, "Give me some one-dollar bills, ten times as many twos, and the balance in fives!"

How did the cashier perform this transaction?

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A Sport Fan's Nightmare

2010-05-14T09:07:00.007-04:00

The sport scene is tense and exciting in Boston this time of year. Celtics playing Cavaliers, Bruins playing Flyers, Red Sox breaking our hearts every night. Sport fans could hardly sleep. When we do fall asleep, we imagine ourselves playing basketball, then growing bats and chewing gum, then the bats morph into hockey sticks and the baseballs turn into packs flying around with a swooshing sound. In a nightmare, you could imagine becoming smaller and smaller and... turning into a baseball ball. You turn your head and see a giant and heavy basketball chasing you. Attempting to escape the orange giant's jumping steps, you (as a baseball), are darting closer and closer to the wall, looking for a corner. Could a baseball hide safely from a basketball in a corner without being "hurt"?

Basketball diameter is 9.39". Baseball diameter is 2.866".

( puzzle adapted from B. Kordemsky book)

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Why "Nine" is "Nine?"

2010-05-14T08:52:00.004-04:00

I watched the movie “Nine” recently, with Daniel Day-Lewis and many amazing actresses. The story is very simple but the movie is worth watching just to enjoy all the beauty on the screen. However, I wonder why it is called “Nine?”

As a second part of this puzzle, I challenge you to recall movies that have digits from one to eight in their titles.

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A Water Puzzle

2010-05-06T14:00:00.012-04:00

This week is all about water in the Boston, MA area. A large pipe supplying drinking water to two million people burst open. While authorities redirected the water supply to come from the local reservoir, people were warned to use this replacement water for bathing but stick to bottled water for drinking. Imagine how fast water disappeared off the shelves of local stores.

This is a puzzle about one local store that ran out of bottled water very quickly, leaving only one large 12 gallon emergency barrel. Two customers grabbed this barrel at the same time and were contemplating how to divide it. The store didn't have any 6 gallon containers, but did have empty 8 gallon and 5 gallon containers. The customers thought for a while but then figured it out. Both went home with 6 gallons of water each. How did they do it?

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Genius Grandkid

2010-05-06T13:21:00.015-04:00

Here is a trick that could help you and your little kid impress a grandma this Mother's Day. A first or second grader is good as they know subtraction, but being able to also do large division wouldn't be suspected. Allow your grandma to use a calculator. Ask her to pick any number. Multiply it by 2, add 5, multiply by 5, and announce the result.

Teach your kid to write the resulting number on a piece of paper. Cross the last digit from this number and subtract 2 from the remaining number to get the number that grandmother picked.

For example: she picks 21.
21 x 2 + 5 = 47
47 x 5 = 235

Your kids takes 235. Crosses out the 5, obtaining 23.
23-2=21

He is genius!
Now, you could be genius if you figure out how does this trick work?

(this trick is from B. Kordemsky book)

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Designing a Soccer Skirt

2010-05-06T11:17:00.012-04:00

Illustration by Mike Baker

My four year old neighbor was strolling along the street wearing an interesting combination of a long flower girl dress and sneakers. I remember how back in my youth in Russia, we used to make fun of this very American style mix. But then I grew up, and moved here. I am trying to be so many things at once and be in so many places at once that I also could be spotted in a very oxymoron combination like sandals, sport leggings and a wide sun hat.

But let's get back to my wonderful little neighbor. Her parents told me that she is wearing sneakers because she had been playing soccer at school earlier. Soccer in this long flower dress??? Yep!

So, what do you think about playing soccer in a dress? How long should the dress be so that it won't be dangerous? Above the knee? Knee high? How wide should be the bottom so that one could run in this dress? Is there any relationship between width and length that would allow optimal mobility and safety?

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Global Boiling

2010-04-29T15:06:00.010-04:00

April 24th, Boston. Crazy weather forecast. Winter to Summer in three days. What single digit can one change so that the daily high temperatures displayed below are in an arithmetic progression?

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Fair Cake Split Among Three

2010-04-29T14:30:00.007-04:00

If you are a lawyer or you have more than one kid, most certainly you are used to "This is not fair!" statements. "Not fair - he got more dessert," "No fair - why should I do chores if she is enjoying life?" etc etc. Imagine that you have something, like a yummy looking chocolate cake or a pile of chocolate sprinkles, that you need to divide among competing parties while minimizing "not fair" statements. When you have two competing parties - two kids - the solution is well-known. You offer one of them to divide the cake into two parts, and then the other one should pick her/his part first. Now, imagine you have three competing parties. Can you think of a creative strategy to help these parties divide their treasure, so that "no fair" screams will be minimized.

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Tile Adventures - Continued

2010-04-29T12:05:00.013-04:00

We are doing renovations at home and a few weeks ago I posted a puzzle about the number of tiles we should buy. We planned on using two sizes of the same tile: 6"x6" and 12"x12" in the pattern depicted below:

With your help, I calculated the number of tile boxes to order; the tiles arrived; we proudly showed them to our contractor; and he said: "That's not good. The pattern is not going to work."
We ended up with a slightly different pattern that I copied from Lowe's bathrooms. Here are our new tiles (still without the grout). Can you guess why we couldn't use the original pattern as planned?

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How many gumballs fit in the machine?

2010-04-29T08:53:00.010-04:00

Inspired by my daughter's wishing for a hot pink gumball and my son's wish for anything but pink, and all the puzzles that followed, I decided to bring a gumball machine to the Cambridge Science Carnival. What could be better than gumballs to demonstrate a fascinating side of math to kids (and many adults)?

I bough a 10" diameter gumball machine and a giant box of 1" gumballs. How many gumballs, approximately, do you think we need to use to fill the machine to the top?

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Regifting Robin: How does it work?

2010-04-21T15:18:00.008-04:00

Tom sent us a nice math trick to demystify. Let's put on our detective hats, click on the image below to see the trick and come back to the Puzzle Marathon to enjoy catching Robin in a fraud and understanding the simple solution.

You pick a two digit number. Let's use letters A and B to define digits in our number. Our number is AB. The value that our number represents is 10 x A + B.
For example, for A=1 and B=5, our number is 10 x 1 + 5 = 15.

Now, Regifting Robin instructs us to subtract both the first and second digit from our number: (10 x A + B) - A - B

Simplifing this we get: 10 x A - A + B - B = 9 x A
For A = 1 we get 9 x 1 = 9
For A = 2 we get 9 x 2 = 18
For A = 3 we get 9 x 3 = 27
Note that continuing with higher As we get all the multiples of 9.

Now we are ready to catch the Regifting Robin in a fraud!
Check Registing Robin's gift table. See what gift is in the cell#9, cell#18, cell#27, and all the other multiples of 9.
What? The same gift???!
No matter what numbers A and B we picked, if we did our math correctly, we get to a cell that is a multiple of 9 and all these cells contain the same gift. No wonder Robin can guess this gift!
Play again and you will see that a different gift is randomly selected but again all the cells that are multiples of 9 have the same gift.

What a fun mass dillusion! Subscribe to our weekly newsletter to get more of such fun tricks by email.

Packing for a sleep-away camp

2010-04-20T14:49:00.009-04:00

Remember the old-fashioned bars of soap? You are trying to figure out whether one would be enough to give to your son for four weeks of the sleep-away summer camp. I know, most of them never wash there, but let's hope that this time he will. You notice that when you leave this soap in the kids' bathroom and check in a week, all of its dimensions seem to erode by two: it has only half of the original height, half of the original width, and half of the original depth. But at home both of your kids are using it, in the camp it will be only for your son. How can you figure whether to pack one or two bars?
(this puzzle is adapted from a book by C. Koval)

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UFO Puzzle

2010-04-20T14:08:00.005-04:00

The astronaut returning from a space walk reported that he found a strange galactic object. It was a perfectly symmetrical solid figure which looked exactly the same no matter what side you approach. At least it did - before the astronaut touched it. Now three of the faces are pulsing with red light, three with blue light, and the other six with green light.

The scientists at base headquarters are still trying to work out what the lights mean, but they do know the shape of each faces. Do you?
(this puzzle is from the Logic Puzzles book by the Diagram Group)

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How many tiles to buy?

2010-04-15T13:40:00.009-04:00

Did you encounter any puzzle last week? Feel free to share it with us. Here is one that we stumbled upon figuring out the amount of tiles to buy to replace the old wood floor at the door entry. The area we want to cover is approximately 90" X 150". We want to use a pattern combining tiles of size 12" x 12" and 6" x 6". One large one and two small on top, creating together a rectangle of 12" x 18". Large tiles are sold in boxes, each holding tiles to cover 10 square foot. Smaller tiles are sold in boxes that each holds tiles to cover 6 square foot. How many boxes of each should we buy?

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Cambridge Incident Puzzle

2010-04-15T13:19:00.008-04:00

Here is a puzzle that is believed to be invented by Albert Einstein as a boy. But don't be fooled by his young age - it is a very hard one!
I adapted it to a contemporary times and local coordinates.

On a single street in Cambridge, MA, stand five houses where live five professors who were all born in different countries: England, Spain, Ukraine, Norway and Japan. All they houses stand in a row, the other part of the street is a park. On April 15th one of the professors found a dead fish in the envelope in his mailbox. Pet shop owner told that one of this professor's neighbors bought this fish alive a few days ago but he didn't remember who exactly. Local police started investigating who was the owner of this fish and therefore responsible for the prank, but kept it very private as high profile people were involved. Here are some pieces of information we were able to fish from the local papers about this street's residents:

1. The Englishman lives in the red house.
2. The Spaniard owns the dog.
3. Coffee is drunk in the green house.
4. The Ukrainian drinks tea.
5. The green house is immediately to the right of the ivory house.
6. The Ford driver owns the snail.
7. A Toyota owner lives in the yellow house.
8. Milk is drunk in the middle house.
9. The Norwegian lives in the first house to the left.
10. The man who drives the Chevy lives in the house next to the man with the fox.
11. A Toyota is parked next to the house where the horse is kept.
12. The Dodge owner drinks orange juice.
13. The Japanese owns a Porsche.
14. The Norwegian lives next to the blue house.

Can you figure out who owned the fish from this information only?

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Swim Rule Logic

2010-04-15T12:01:00.006-04:00

I went swimming yesterday and was sharing a lane with another Medium level swimmer that was using flippers. As soon as the life guard saw the wide splashes he was making with his flippers, she ordered us to circle in the lane instead of splitting the lane. Usually two swimmers would split and each swim in his/her column while three or more swimmers would circle. I thought at first, of course it makes sense - we will pass each other much less when circling. But then I got doubtful. What do you think? Do you see any logic in this swimming rule?

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Archimedes' Grave

2010-04-09T07:57:00.008-04:00

Archimedes made a plenitude of significant scientific discoveries throughout his life. He designed machines capable of lifting attacking ships out of the water as well as mirror arrays capable of focusing sun rays and setting enemy ships on fire. He explained why and how bodies float in the water, helping the king verify that his crown is indeed made out of pure gold. He was fascinated with infinity and found the way of approximating the number Pi as well as counting the number of grains of sand that will fit inside the universe. He died telling a Roman soldier that he is too busy to meet a general as he was contemplating yet another mathematical diagram. His tomb was decorated with his favorite discovery .... What do you think it is? Explain why to get a puzzle point.

Who ate the cake? Who? Who?

2010-04-08T22:10:00.011-04:00

One of you two, out there, ate the last piece of cake we were hoping to save for grandma. I can figure out who did it without even checking your sticky fingers and dirty teeth. Whoever did it, pick any odd number. Whoever didn't do it, pick any even number. But be honest! Now, you, standing closer to me, multiply your number by 2. The other person - multiply your number by 3. Share your numbers with each other and tell me their sum. As soon as I hear this sum, I can now figure out who ate the cake! How?

(this puzzle is inspired by a story from B. Kordemsky book)

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!

How far would you drive for a family dinner?

2010-04-08T21:53:00.008-04:00

April is the time of travel: Passover dinners, Easter brunches, school vacations or just life-is-beautiful-again weekend trips. A friend complained to me that she spent five hours in the car last week, driving to her mother's house and back for a holiday family gathering. On the way there traffic was terrible due to flooding and she averaged only 20 mph. On the way back, it was a little better averaging 30 mph. How far away do you think her mother lives?

This puzzle is adapted from A. Salny's book (Super Smart Super Puzzle Book #2)

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!