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D I J K L A J

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F J O P P Q G

H F A R K J B

I also like gym, but rarely go there: it doesn’t work out. I stopped using stairs, because they are up to something. I wanted to learn how to juggle, but I don’t have the balls to do it.

I work at MIT, the work place with the best dam mascot: Tim the Beaver. My salary is not big, and I stopped saving money after I lost interest. I’m no photographer, but I have pictured myself outside of MIT too. I am a mathematician, which is the most spiritual profession: I am very comfortable with higher powers. I praise myself on great ability to think outside the box: it is mostly due to my claustrophobia. I am also a bit of a philosopher: I can go on talking about infinity forever.

I would love to tell you a joke. I recently heard a good one about amnesia, but I forgot how it goes.

My biggest problem is with English. So what if I don’t know what apocalypse means? It’s not the end of the world!

I never get tired of puns and here is my list of pun puzzles from the MIT Mystery Hunt:

- We Are All Afraid to Die. I edited this 2018 puzzle and enjoyed it very much.
- Mass Aid. I didn’t work on this 2018 puzzle, but it looks like a lot of fun.
- Capital Punishment. 2017 puzzle that looks tempting.
- Typecasting. A 2017 puzzle with pictures of actors.
- Losers. A 2016 puzzle that I would be very bad at.
- Be a Star!. A 2015 puzzle that I enjoyed very much.
- Feeling Bluefin. A 2015 puzzle that looks delicious.
- Timbales. A 2011 puzzle that might be the most famous pun puzzle.

Business plan:

- Sign-up for a premium-rate telephone number through which you make money from every call.
- Take a loan at the bank.
- Do not pay back.
- Collection agencies start calling non-stop.

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- TMake a full-body selfie.
- Eat greedily for a year.
- Take a full-body selfie again.
- Swap before and after.
- Post.
- Collect the likes.
- Give diet advice.

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A cafe patron ordered a pastry, then changed his mind and replaced it with a cup of coffee. When he finished his coffee, he started leaving without paying. The waiter approached him:

—You didn’t pay for coffee!

—But I had it instead of the pastry.

—You didn’t pay for the pastry either!

—But I didn’t have the pastry.

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At a farmers market stand there is a sign: 1 melon—3 dollars, 3 melons—10 dollars. A client requests one melon and pays 3 dollars, then repeats the procedure two more times. Then he says: “I bought three melons for 9 dollars, while you are trying to sell them for 10 dollars. This is really stupid.” The farmer talks to himself: This happens all the time: they buy three melons instead of one, and try to teach me how to make money.

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If the government listens in on my phone conversations, should they be paying half of my phone bill?

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To get to free downloads, please, enter your credit card number.

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The biggest lie of the century, “I have read and agree to the terms of …”

* * * (submitted by Sam Steingold)

Ignorance: If your poker opponent got lucky cards four times in a row, he must get lousy cards now.

Knowledge: Nope, the deals are independent; prior observations have no bearing on the next deal.

Wisdom: The opponent is cheating; get away from the table now!

Problem 1.Is it possible to put positive numbers at the vertices of a triangle so that the sum of two numbers at the ends of each side is equal to the length of the side?

One might guess that the following numbers work: (a+b-c)/2, (b+c-a)/2 and (c+a-b)/2, where a, b, and c are the side lengths. But there exists a geometric solution: Construct the incircle. The tangent points divide each side into two segment, so that the lengths of the segments ending at the same vertex are the same. Assigning this length to the vertex solves the problem. Surprisingly, or not surprisingly, this solution gives the same answer as above.

Problem 2.Prove that it is possible to assign a number to every edge of a tetrahedron so that the sum of the three numbers on the edges of every face is equal to the area of the face.

The problem is under-constrained: there are six sides and four faces. There should be many solutions. But the solution for the first problem suggests a similar idea for the second problem: Construct the inscribed sphere. Connect a tangent point on each face to the three vertices on the same face. This way each face is divided into three triangles. Moreover, the lengths of the segments connecting the tangent points to a vertex are the same. Therefore, two triangles sharing the same edge are congruent and thus have the same area. Assigning this area to each edge solves the problem.

There are many solutions to the second problem. I wonder if for each solution we can find a point on each face, so that the segments connecting these points to vertices divide the faces into three triangles in such a way that triangles sharing an edge are congruent. What would be a geometric meaning of these four points?

Share:]]>I already posted an essay about the puzzles I wrote myself. Four of my five puzzles are math-related, so I am including them below for completeness. I will mention the topic of each puzzle unless it is a spoiler.

I start with Nikoli-type puzzles. Four elegant Nikoli-type puzzles were written or cowritten by Denis Auroux. In all of them the rules of the logic are stated at the beginning. That means the logic part doesn’t contain a mystery and can be solved directly.

- Good Fences Make Sad and Disgusted Neighbors (by Denis Auroux). You can guess by the title that this puzzle was in the emotions round corresponding to sadness and disgust. This is an interesting variation on the hexagonal Slitherlink. This is a relatively easy puzzle.
- Shoal Patrol (by Denis Auroux and James Douberley). Each grid is a combination of Battleship, Minesweeper, and a loop puzzle. These are difficult, but satisfying puzzles. The extraction step is not mathematical and not completely trivial.
- Submarine Patrol (by Denis Auroux and James Douberley). This is a 3D version of Shoal Patrol.
- Hashiwokakuro (Count your bridges) (by Denis Auroux). This is a mixture of Hashi and Kakuro. I enjoyed the puzzle while I tested it. The extraction is trivial.
- A Learning Path (by Tanya Khovanova and Xavid). This is a path logic puzzle that was targeted for new hunters. It contains self-referencing hints and solving techniques.

There were several puzzles that were very mathematical.

- X Marks the Spot (by Zachary Chroman). A very non-trivial puzzle about triangle centers.
- Tournament Organization (by Scott Harvey-Arnold ). A tournament reconstruction puzzle.
- Cash Cab (by Erica Newman and Justin Melvin).
- Voter Fraud (By Ben Weissmann). A voting puzzle.
- The 10,000 Puzzle Tesseract (by Charles Steinhardt, Zachary Chroman, and Scott Harvey-Arnold ). The most difficult puzzle of the hunt, by far.
- Games Club (by Tanya Khovanova and Sergei Bernstein). This puzzle is about combinatorial two-player games.
- Murder at the Asylum (by Tanya Khovanova). This is a difficult puzzle about liars and truth-tellers.
- Studies in Two-Factor Authentication (by Brandon Avila). A very elegant puzzle, that is one of my favorites.

There were also some math-related or computer-sciency puzzles.

- The Next Generation (by Colin Liotta). I enjoyed being an editor of this puzzle.
- Disorientation (by Alex Churchill). This puzzle has a beautiful visual component.
- Message in a Bottle (by Nathan Fung). The puzzle doesn’t look like it has something to do with mathematics, but my testing of it was very satisfying. I guessed from the start what it was about.
- Self-Referential Mania (by Justin Melvin). Self-referential logic puzzle, which I enjoyed editing.
- Bark Ode (by Elizabeth French, Justin Melvin, and Erica Newman). The pictures are so cute.
- Executive Relationship Commandments (by Robin Deits, John Toomey, and Michele Pratusevich). I didn’t see this puzzle until after the hunt. I wish I could have tested this puzzle with my son Alexey, who is a computer scientist.

There were also several decryption puzzles:

- Word Search (by Tanya Khovanova). A crypto word search.
- Texts From Mom (by Elizabeth French and Justin Melvin ). A text enciphered with emojis.
- Marked Deck (by Colin Liotta and Leland Aldridge). One of my favorite puzzles. Hunters received a physucal deck of cards that was laser cut. You can buy the deck at Etsy. The art in this puzzle is beautiful, but the puzzle also has a non-trivial decryption step.

Puzzle.Five pirates discovered a treasure of 100 gold coins. They decide to split the coins using the following scheme. The most senior pirate proposes how to share the coins, and all the pirates vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the next most senior pirate making a proposal.As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins whether he votes for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all five pirates are intelligent, rational, greedy, and do not wish to die, how will the coins be distributed?

You can find the solution in many places including Wikipedia’s Pirate game. The answer is surprising: the most senior pirate gets 98 coins, and the third and the fifth pirates by seniority get one coin each. I always hated this puzzle, but never bothered to think through and figure out why. Now I know.

This puzzle emphasizes the flaws of majority voting. The procedure is purely democratic, but it results in extreme inequality.

That means a democracy needs to have a mechanism to prohibit the president from blatantly benefiting himself. With our current president these mechanisms stopped working. Given that Trump does everything to enrich himself, the pirates puzzle tells us what to expect in the near future.

We, Americans, will lose everything: money, clean air and water, national parks, future climate, health, social security, and so on, while Trump will make money.

Share:]]>- A Learning Path (jointly with Xavid) is a Nikoli-type logic puzzle that was targeted for new hunters. It contained self-referencing hints and solving techniques. It was in both disgust and fear.
- Word Search is a word search with a twist. The words are related to fear and sadness.
- Games Club (jointly with Sergei Bernstein) is a puzzle on the topic of combinatorial two-player games. It is pure sadness.

I also wrote another easy puzzle called A Tribute: 2010-2017 (jointly with Justin Melvin, Wesley Graybill, and Robin Diets ). Though the puzzle is easy, it is useful in solving it to be familiar with the MIT mystery hunt. This is why the puzzle didn’t fit the first emotions round.

I also wrote a very difficult puzzle called Murder at the Asylum. This is a monstrosity about liars and truth-tellers.

Share:]]>

Problem.A number has three hundred ones and three hundred zeroes. Can it be a square?

The solution goes like this. Consider divisibility of this number by 9. The sum of the digits is 300. That means the number is divisible by 3, but not by 9. Therefore, it can’t be a square.

Why do we consider divisibility by 9? The divisibility by 9 is a very powerful tool, but why was it the first thing that came to my mind? The divisibility by 9 doesn’t depend on the order of the digits. Whenever I see a problem where the question talks about digits that can be in any order, the first tool to use is the divisibility by 9.

The why question, is very important in mathematics. But it is also very important in life. It took me many years to start asking why people did this or that. I remember my mom was visiting me in the US. Every time I came back from work, she complained that she was tired. Why? Because she did the laundry in the bath tub. She wouldn’t use my washing machine, because she didn’t have such a thing in Russia. I promised her that I’d do the laundry myself when there was a sufficient pile. However, she insisted that the dirty clothes annoyed her. I would point that my water bill went up. And so on.

We argued like this every day. We were both frustrated. Then I asked myself why. Why does she do the laundry? The answer was there. She wanted to be helpful. I calmed down and stopped arguing with her. I sucked it up and paid the water bills. Her time with me turned into the most harmonious visit we ever had. Unfortunately, it was the last.

Share:]]>**Puzzle.** Alice, Bob, and Charlie are at Alice’s house. They are going to Bob’s house which is 33 miles away. They have a 2-seat scooter which rides at 25 miles per hour with 1 rider on it; or, at 20 miles per hour with 2 riders. Each of the 3 friends walks at 5 miles per hour. How fast can all three of them make it to Bob’s house?

I can count to 1023 on my 10 fingers. The rudest number is 132.

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I kept forgetting my password, so I changed it to “incorrect”. Now, when I make a mistake during login, my computer reminds me: “Your password is incorrect.”

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—You promised me 8% interest, and in reality it is 2%.

—2 is 8—to some degree.

* * * (submitted by Sam Steingold)

Quantum entanglement is simple: when you have a pair of socks and you put one of them on your left foot, the other one becomes the “right sock,” no matter where it is located in the universe.

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Teacher:

—I keep telling my students that one half can’t be larger or smaller than the other. Still the larger half of my class doesn’t get it.