Mathematics, applications of mathematics to life in general, and my life as a mathematician.
Let me begin with labeled chip-firing on an infinite directed binary tree, where the root is at the top. Place 2n chips, labeled from 0 to 2n − 1, at the root. A move consists of choosing any two chips at the same vertex and firing them: the smaller chip goes to the left child, [ ]
For the last homework of the year, I gave my students a killer puzzle—literally. Puzzle. A mysterious man kidnaps people, takes them to his cabin, and offers each victim two identical-looking pills. He claims that one pill is poisonous and the other is harmless. The victim chooses one pill, swallows it with water, and dies, [ ]
Here is another puzzle posted on Facebook by Konstantin Knop. Share:
I asked ChatGPT to tell me some jokes about itself. Here we go. * * * ChatGPT never loses an argument.It simply generates a more confident version of the same mistake. * * * I asked ChatGPT for a brief answer.It said, “Absolutely!” and then divided the answer into twelve sections. * * * ChatGPT [ ]
Konstantin Knop wrote to me about a weighing puzzle. Apparently, the balance scale keeps inserting itself into our conversation. Puzzle. There are several coins, each weighing either 10 grams or 11 grams. Determine the parity of the number of coins of each weight using a balance scale. Given the total number of coins, it is [ ]
I gave the following problem as part of the entrance test for my STEP program. Puzzle. What word would you use to describe a man who does not have all his fingers on one hand? The test had 17 questions, and this one was the only trick question. My goal was to check whether the [ ]
Here is a new puzzle by Nikolai Chernyatiev. Puzzle. Five sages, who all know one another, are blindfolded, seated in a row in a dimly lit hall, and then have their blindfolds removed. Each sage can see both of their immediate neighbors, but no farther; the sages at the ends know that they are at [ ]
Alexander Karabegov sends me new puzzles from time to time. This time, however, it is not a puzzle but a math joke. Joke. If a woman gives birth to a child at the age of 30, then 60 years earlier, her child was twice as old as she was. Whatever that means. Share:
I ve been staring at my icosahedron, trying to solve the following puzzle by Konstantin Knop. Puzzle. One face of an icosahedron is special. The numbers 2, 3, and 5 are written at its vertices in some order. All other vertices of the icosahedron are labeled with 1. In one query, we may ask an oracle [ ]
Puzzle. A ball rolls forever on a frictionless billiard table with no pockets. Can you find a finite convex shape of the table for which no trajectory of the ball ever covers the entire surface? Share: