Tanya Khovanova's Math Blog

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, and the larger chip goes to the right child. For k ≥ 2, the k-a...

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, while the killer consume...

Here is another puzzle posted on Facebook by Konstantin Knop.

Puzzle. One day, three inhabitants of the Island of Knights and Liars invited a foreign correspondent to visit so that they could tell him about their island. Knights always tell the truth, while liars always lie.

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 went to th...

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 enough to fin...