Another Simple Logical Puzzle

OK, I got it. We like it simple. Two weeks ago when I posted  A Simple Puzzle over twenty readers dared to answer. I also noticed that when I post logical puzzles more answers are coming from women.  So, let's try something simple and logical.  This puzzle was suggested by our expert puzzle solver - Ilya.  Thank you!

Observe four cards. They all have a number on one side and either red or brown color on another.  Two are turned to the number side and have numbers 3 and 8 and two are turned to the color side and are correspondingly red and brown. 

Your friend is saying that among these four cards all the cards with even number on them have a red backside.  Is she right or wrong? What card(s) do you need to flip to confirm or reject her statement? Try flipping as less cards as possible.

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

A Dinner Puzzle

Recently at a dinner party the hostess offered the following puzzle for anyone interested. Assume you have two numbers: a and b. Create a math sentence using these numbers and the +,-,/,*, square root and power signs so that this sentence will produce the largest of these numbers as the output.

The hostess told that this puzzle was offered to her a day before and she couldn't concentrate for a number of hours till she solved it. Needless to say, I also do not remember what was served at this dinner or the names of the guests. It took a whole evening and finally at 11:30pm the angel of solution descended upon me. Can you catch him as well?

Image by Amelia-Jane, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.  

Skiing Puzzle

A very cute puzzle from a great book by Ian Stewart "Professor Stewart's Cabinet of Mathematical Curiosities."

The little known village of Apres-le-Ski is situated in a deep mountain valley with vertical cliffs on both sides. The cliffs are 600 meters high on one side and 400 meters high on the other. A cable car runs from the foot of each cliff to the top of the other cliff, and the cables are perfectly straight. At what height above the ground do the two cables cross?  To make your explanations easier I marked with "h" the height we are looking for and with "a" and "b" parts of the base that you may want to use in your calculations. Remember that "h", "a" and "b" are all unknowns and we want the answer for "h" as a number.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Parking Behavior

This might have happened to you. You drive to a meeting or a store and observe that the adjacent open parking lot is completely full. You know that in the next 5 mins at least one parking spot will definitely open, but there is 50% chance that someone else will snatch it. You are considering your options:

1) park in the neighboring multi-floor closed garage for $15 and take extra 5 mins to get out of the garage (possibly feeling like a loser when you see that a few spots in the open lot became open)
2) sit in a the car and wait patiently until someone returns to their car around you and grab their place
3) drive around the open parking lot trying to spot someone who returns to their car, follow this person and aggressively take their place fighting with competitors

What option will you choose and why? Our behavior in such situations can be described with a mix of psychology and math. Perhaps more of the former. Let's see. What would you do?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Top image by Ronan_tlv, distributed under CCL.

How long is the movie

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.

Dead presidents: spell or coincidence?

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.

A Water and Oil Puzzle

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.

Meet me at Marshalls

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.

A Truly International Company

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

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.

Cookies and Milk

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.

Math can save lives, admiral!

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?

Airport Games

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!

Best Document Review Strategy

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.

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

Bullfight in Barcelona

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?

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

The Case of the Arctic Hero

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?

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

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

Easy Money

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.

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

Guess My Phone Number - a tribute to M.Gardner

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.

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

Doctor's Dilemma

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?

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

A Sport Fan's Nightmare

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)

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