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Answer to Test Your Intuition 50: Detecting a Deviator
Two weeks ago we asked: Ruth and Ron start together at the origin and take a walk on the integers. Every day they make a move. They take turns in flipping a coin and they move together right or left...
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Test Your intuition 51
Suppose that and are two compact convex sets in space. Suppose that contains . Now consider two quantities is the average volume of a simplex forms by four points in drawn uniformly at random. is the...
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Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic...
Bo’az Klartag (right) and Joseph Lehec (left) In December 2020, we reported on Yuansi Chen breakthrough result on Bourgain’s alicing problem and the Kannan Lovasz Simonovits conjecture. It is a...
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ChatGPT Meets Elchanan Mossel’s Dice Problem
One of the greatest hits of this blog was Elchanan Mossel’s dice problem, asked here and answered here. Here is how chatGPT (the free version) handles the problem. You throw a die until you get 6. What...
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TYI 54: A Variant of Elchanan Mossel’s Amazing Dice Paradox
The following question was inspired by recent comments to the post on Elchanan Mossel’s amazing Dice Paradox. A fair dice is a dice that when thrown you get each of the six possibilities with...
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Test Your Intuition 55: The Case of Two Screening Tests
Here is a great question invented by Michele Piccione and Ariel Rubinstein. (Let me use this opportunity to recommend their mind boggling 1997 paper on the absent-minded driver.) The question (TYI 55)...
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Test Your Intuition 56: Fifteen Boxes Puzzle
Andrew and Barbara are playing a game. Fifteen boxes are arranged in a 3-by-5 grid, labeled with the letters A through O, as shown below. A B C D E F G H I J K L M N O The organizers of the game have...
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Timothy Chow’s Amazing Fifteen Boxes Puzzle (TYI 56)
TYI56 asked the following question of Timothy Chow: You have fifteen boxes labelled with the English letters from A to O. Two identical prizes are placed in two (distinct) boxes chosen at random....
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Jiaoyang Huang, Theo Mckenzie, Horng-Tzer Yau: Ramanujan Property and Edge...
A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of random d-regular graphs G with vertices. The following paper marks a huge leap in our...
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Annotated Pictures from Fall 2024
Apart from pictures, I write about the very first “Test your Intuition” question, a pioneering work of Tutubalin, the hierarchy of valuations of Lehman, Lehman, and Nisan, and three conjectures of Miki...
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