Archive for the ‘Puzzles’ Category.

## Fast Thinking

How much time will it take you to answer the following question?

Can the equation 29x + 30y + 31z = 366 be solved in natural numbers?

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## Puzzle Ninja

Alex Bellos sent me his new book Puzzle Ninja: Pit Your Wits Against The Japanese Puzzle Masters. What has he done to me? I opened the book and couldn’t close it until I solved all the puzzles.

This is a fantastic book. There are many varieties of puzzles, including some types that I’ve never seen before. Also, the beautifully designed puzzles are great. Often puzzles of the same type target different solving ideas or have varied cool themes.

This book is more than a bunch of puzzles; it also contains poetic stories about puzzle histories and Japanese puzzle designers. Fantastic puzzles together with a human touch: this might be my favorite puzzle book.

I present two puzzles from the book. The puzzle type is called Wolf and Sheep Slitherlink. The Slitherlink is a famous puzzle type with the goal of connecting some of the neighboring dots into a single non-self-intersecting loop. A number inside a small square cell indicates how many sides of the square are part of the loop. Wolf and Sheep Slitherlink is a variation of Slitherlink in which all sheep should be kept inside the fence (loop) and all the wolves outside.

Ignore the numbers in the title as they just indicate the order number of Wolf and Sheep Slitherlink puzzles in the book. The number of ninja heads shows the level of difficulty. (The hardest puzzles in the book have four heads.) The difficulty is followed by the name of the puzzle master who designed the puzzle.

The first puzzle above is slightly easier than the second. I like the themes of these two puzzles. In the first one, only one cell—lonely wolf—marks the relationship to the fence. In the second one, the wolf in the center—who needs to be outside the fence—is surrounded by a circle of sheep who are in turn surrounded by a circle of wolves.

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## An Orchestra Puzzle

An orchestra of 120 players takes 70 minutes to play Beethoven’s 9th Symphony. How long would it take for 60 players to play the symphony?Share:

## Mafia Logic Puzzle

I found this puzzle on the Russian QWERTY channel.

Five people sit around a table playing Mafia. Among them are two innocent people, two Mafiosos, and one detective. The Mafia people know each other; the detective knows who each of them is; and the innocent people have no information whatsoever about anyone at the table.

During this particular game, the innocents and the detective always tell the truth, while mafia people always lie. They start by going around the circle making the following statements:

• A: I know who B is.
• B: I know who the detective is.
• C: I know who B is.
• D: I know who E is.

Who is who?

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## Another Cool Coin-Weighing Problem

My coauthor, Konstantin Knop, sent me a coin-weighing problem that is really good. Surprisingly, it is old: it first appeared in a Russian math journal, Kvant, in 1973.

Puzzle. At a trial, 14 coins were presented as material evidence. The expert tested the coins and discovered that seven of them were fake, the rest were real, and he knew exactly which coins were fake and which were real. The court only knows that counterfeit coins weigh the same, real coins weigh the same, and fake ones are lighter than real ones. The expert wants to use not more than three weighings on a balance scales without weights to prove to the court that all the counterfeit coins he found are really fake, and the rest are real. Could he do it?

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## I am on TEDEd

A cartoon based on my script is posted on TEDEd: Can you solve the Leonardo da Vinci riddle?.Share:

## A Self-referencing Multiple-Choice Question

There is only one correct answer to this puzzle. Choices:

1. The correct answer is B).
2. The correct answer is C).
3. The correct answer is A).
4. The correct answer is D).

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## Looking for the Cutest Answer

Puzzle. A boy fell off of a 30 meter ladder, but didn’t get hurt. Why not?Share:

## My Last Visit with John Conway

John Conway came to the 2017 MOVES conference and told me that he wanted to talk to me about subprime fibs. The subprime Fibonacci sequence was invented by John Conway, and I wrote a paper about it. The paper, Conway’s Subprime Fibonacci Sequences, wasn’t written with John, but rather with Richard Guy and Julian Salazar, and is published in Mathematics Magazine.

I wanted to visit my friend Julia, who lives in Princeton, and this was a good opportunity to discuss the mysteries of subprime fibs with John. On my second day in Princeton, I came to the math department around 3:00 pm carrying some apples. John never goes out for lunch, as he has trouble walking, so he is always hungry by the end of his work day. Thus, each time I go visit him, I come with food. We have very different tastes in apples: unlike me, he likes his apples unwashed.

Anyway, by the time I arrived to the department, John had already left. This was somewhat unusual, so I called him. He sounded weird and not very coherent, as if he wasn’t feeling well. Considering also that he had left early, I started to worry. Unfortunately, there was a lot of background noise during our conversation and I only understood that he was at a pizza place. John walks very slowly, so he couldn’t have gone too far away from campus. I found him in the second pizza place I checked. It was Tiger’s Pizza. He told me that he felt very sleepy and tired. However, I was gratified to see how much having an interested listener gave him energy. He started telling me stories of his trip to Germany a long time ago. He had already eaten, but decided to have some more fries. As a perfect gentleman he offered me some, but I didn’t want any.

At some point he dropped a couple of fries on the floor. He tried to reach them and I jumped to help. That was a mistake. I actually know that he likes proving to me and to himself that he can do stuff independently. He accepts my help when I am subtle about it, or when it is unavoidable. Anyway, he looked at me angrily and I backed off. He picked up his fries from the floor and ate them.

I liked his T-shirt and tried to take a picture of it. As you can see, I am no photographer. The T-shirt shows a test question: Name the triangles. Then it features three triangles: an equilateral, isosceles, and right. It also provides someone’s answers to this naming test: Geoffrey, Frederick, Eugene.

John asked me if I am more scared of Donald Trump or Kim Jong Un. We agreed that Trump is scarier. At this time he seemed his usual self.

I offered John a ride home, as I do whenever I visit him. He was very glad as he felt very tired. He started to get up. This time, I remembered not to try to help. He couldn’t get up, I waited. He tried to push his weight off the table top, but the table was wobbly. I leaned on the table, as if to rest. We often play this sort of game in which he welcomes my help as long as we both pretend that I’m not helping.

My car was a block away and he wanted to walk the block. But after making two steps out of the pizzeria he changed his mind and asked me to bring the car to him. This was the first time ever. This visit he was so much worse than ever before.

On the drive to his place, he gave me a puzzle:

John’s puzzle. Given a Mebius strip with a hole, how do you embed it in 3-D so that the two circular borders of the surface are equivalent?

I dropped him off at his house and offered to walk him to the door. He refused. I sat in my car and watched him walking very slowly along his path. I had this sinking feeling in my gut that I was seeing John for the last time. I drove away, once he disappeared behind his door.

On my way back to Boston I visited my friend Vitaly in East Brunswick, and the next day my high school friend Olga in Edison. In Edison, my car started beeping and I panicked. I was far away from home, and didn’t want to be stuck in NJ. I started to look for the source of the sound. It was John’s phone. As always, my gut feeling deceived me: I had to go back to Princeton.

I drove back to John’s apartment. His door was unlocked and I entered. He was resting in bed. He was greatly annoyed at being disturbed. I explained the reason, and gave him his phone. He took the phone and said, “Off you go.” I had this sinking feeling in my gut that these words would be the last words that I would hear from John.Share:

## A Crypto Word Search for G4G13

Here is the crypto word search I designed as a gift exchange for G4G13 (Gathering for Gardner). The submitted file is here: Crypto Word Search.

A B C D E F G
H C I F B B C
D I J K L A J
C I F M A C K
N O O N F B I
F J O P P Q G
H F A R K J B
The words are: ART IDEA MAGIC MATH NOTE PI PROBLEM PUZZLE RIDDLE TRICK.Share: