Tanya Khovanova's Math Blog

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:

I gave the following puzzle to my students. Puzzle. A cowboy rides into town on Friday, stays for three days, then leaves on Friday. How come? Most of them submitted the standard answer: his horse is named Friday. One student suggested that the town was named Onfriday. This solution works well when the puzzle is […]

I am so happy that I met Ivo David and Yogev Shpilman. Together, wrote the book Mathematical Puzzles and Curiosities, and had so much fun on the way. I have already mentioned one of the puzzles from the book on my blog—Two Points on a Cube. Here is another one. Puzzle. Consider the sequence: O, […]

Puzzle. Two fathers gave money to their sons. The first father gave $200, and the second father gave $100. Yet the total amount received by the sons was only $200. How come? Standard answer: There were three people: a son, his father, and his grandfather. The grandfather gave the father $200, and the father gave […]

In the homework for my STEP program, I gave the following challenge problem. Puzzle. My sages each wear a hat of a different color. As in standard hat puzzles, they can see everyone else’s hat color. Unlike in many other hat puzzles, they know the color of their own hat as well. I announce which […]

In a recent post, Each Point has Three Closest Neighbors, I mentioned the following conjecture. Karabegov’s Conjecture. Any finite planar point configuration in which every point has exactly 3 closest neighbors must contain at least 16 points. The conjecture was proposed by my dear friend Alexander Karabegov, whom I met in 1974. Wait. What?! I […]

Every year, after the PRIMES program begins, I send a letter to our students about how to read a math paper. The students in my group are juniors just starting their research. They are often required to read advanced math papers—frequently the first research papers they have ever encountered. This year, I decided to post […]

My goal is to expand my students’ minds. So, though my STEP program is about mathematics, I sometimes give problems from other areas for homework. Here is a recent physics one. Puzzle. You have a brick of 1 kilogram. How does the weight of the brick change during the year? As always, my students generated […]

Here is a probability puzzle I heard from my son Sergei. We even included this puzzle in our book Mathematical Puzzles and Curiosities. Our book includes the answer but omits the details. So, this blog post is devoted to said details. Puzzle. Alice rolls a die until she gets 6. Then Bob observes that she […]

I wrote a book. This is my first book, so I am very proud. I wrote it together with two brilliant puzzle lovers, Ivo Fagundes David de Oliveira and Yogev Shpilman. The book is published by World Scientific and is available for pre-order: Mathematical Puzzles and Curiosities. Here is one sample puzzle from the book. […]