Parrots and Cages puzzle

You have 42 parrots and 7 cages of various sizes. Lock all the parrots inside the cages so that no cage is empty and each cage contains an odd number of parrots.

A hint: this puzzle requires some unusual thinking.

Warning: the solution is below.

At first it seems simple: 42 divide by 7, 6 parrots in each cage. But the number of parrots in each cage should be odd. OK, let's try 1 parrot in each of the first 6 cages. How many parrots are left? 42-6=36. Put 36 in the last cage. Again, not an odd number. 

Now we note that in general, there is no way that 7 odd numbers could be added to produce an even number. So, there must be a trick! A trick that does not involve the numbers. 

And the trick is to place cages inside each other. There was a note of cages being of different sizes. So, place one parrot inside a small cage, place this cage inside a large cage. Both cages have odd number of parrots. You are left with 41 parrot and 6 cages. Now, it is easy. Anyway you do it, it works. Just keep numbers odd.

You can try this puzzle now on your friends and family if you are not afraid to be beaten.  A simpler version of it is to pack 6 presents inside 7 boxes of various sizes so that no box is empty.

Enjoy!

Bermuda Triangle Puzzle

I should warn you that this is a tricky one.  It came via Facebook and god knows what devil invented it but as all the good puzzles it is carefully retold through generations and social networks.

Two triangles consist of exactly the same shapes. Shaped are rearranged in a different order in the bottom triangle and suddenly... one square disappears. How did this "Bermuda Triangle" swallowed the square?

Fill free to print the pictures and play with them, use a ruler. Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. You can also email me your drawings to maria@themathmom.com

Kids Magic Trick

This came in a magic trick box that our daughter picked for her birthday.  Exhausted from all the Bar Mitzvah preparations for her older brother and her own demands for a Harry Potter birthday party, we didn't have any time to buy her a present or even think of anything original to serve as a present. As soon as she realized that no wrapped packages should be expected, she pragmatically proposed that on our next trip to a toy store she will pick something that she likes, I will wrap it and we all pretend it was a surprise.

She chose two sale boxes: one with a hundreds of hip-hop tattoos and another with magic tools. Among dice, fake nails and blood in the magic box there were these cards. 

Now, pay attention, because it starts to be complex. 

Our daughter, the magician, would ask you to think of a number between 1 and 63. Do not reveal this number!

Then, she will show you these cards, one-by-one.

After seeing each card you will say whether the number you picked is on this card or not.

And then, after these 6 yes-no answers, she will guess your number!

Let's try. 

I pick 23.

A-yes

B-yes

C-yes

D-no

E-yes

F-no

She magically guesses: 23!

How does she know?

Quite simple. The instructions on this magic set tell her to add up all the left corner numbers from the "yes" cards.

A+B+C+E

1+2+4+16=23

Unbelievable!

Try it yourself and think how this could possibly work. Two puzzle points for any lead here.

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

Confusion Play

Things are not always what they seem. Take this:

Red  Blue Green Yellow

Is the Red red, Blue blue, Green green and Yellow yellow?
Now, consider this statement:

SEVEN
- NINE
---------
 EIGHT


Definitely false!
Believe it or not but the statement is true if each letter is replaced with a different digit. In fact there are two different ways to decode this subtraction. Can you find both solutions?

If the above statement can be true, what about this:

SEVEN
+NINE
--------
EIGHT


Turns out this one is always wrong. No matter how you substitute the digits for letters. Can you tell why?

(both arithmetic operations come from a book by C.R.Wylie Jr. "101 Puzzles in thought and logic")

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

Beware of the Friendly People

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.

Dating Math Puzzle

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?

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How Long is the Traffic Jam?

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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Mathematician in the Law School

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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The Thieving Clown

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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Metal Water Bottlle in the Dishwasher?

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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How long did he live?

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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Sam Loyd's Cashier Puzzle

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 Water Puzzle

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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Fair Cake Split Among Three

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.

Image via Flickr by terren.
Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize! One puzzle per week, please.

Cambridge Incident Puzzle

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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Archimedes' Grave

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.

Matzo Balls Puzzle

Who doesn't love chicken soup? How about a special but rare treat of chicken soup with Matzo balls? During the recent Passover celebration my kids were helping me to roll these balls from the Manischewitz Ball Mix. According to the package directions, it was enough to make around 10 balls of diameter 1". We had two packs and I realized that it is not going to be enough as kids wanted to have more than two for everyone. We decided to make the Matzo balls smaller, with 0.5" diameter. Can you help me to estimate how many balls we will end up having?

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A Very Advance Reservation

You are waiting for an appointment in the doctor's office and it looks like she is running late. Unfortunately, your iPhone (or Blackberry) battery is out and other than a Fly Fishing Magazine, all are taken. You suddenly become preoccupied with your son's Bar Mitzvah that is still three years ahead, but you need to reserve a place. You are trying to figure out what day of the week his birthday will fall on in 2013. It falls on Thursday this year, 2010. Is it humanly possible to deduce this without a calendar?

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Weigh, then Steal and Kill

Hollywood producer of a new "Steal and Kill" movie noticed that nine golden bricks and eleven silver bricks weigh the same. However, when he took one golden and one silver brick from their piles and switched them placing silver brick into gold pile and gold brick into silver pile, golden pile became lighter. In fact, he had to add his iPhone to the gold pile to make it weigh the same as silver. What is the weight of each, golden and silver bricks? Assume iPhone is 133 g.

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Michelle Obama's Plane

Michelle Obama was returning from LA on a 747 and her White House Chief of Security planned to pick her at the airport in a special bulletproof car. Obama's plane landed ahead of schedule and the security chief unaware of it was still on his way. Michelle took a congressman's limousine back home. Fifteen minutes later security chief car intercepted the limousine on the way and asked the First Lady to switch cars. She was so happy to be back at the White House twenty minutes earlier than scheduled. When Washington chief of security had to file a day progress report, he was at loss as to when exactly the plane landed. The original schedule stated landing at 3.30pm. Can you help him?


This is a fictional story. The puzzle is adopted from the book by B. Kordemsky

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