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Category Archives: Test your intuition
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 probability 1/6. A random dice is … Continue reading
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 is the expected … Continue reading
Posted in AI, Probability, Riddles, Test your intuition
Tagged AI, ChatGPT, Elchanan Mossel
17 Comments
Test Your Intuition 53 by Ehud Friedgut: Which Way to Ride Your Bike
This post was kindly written by Ehud Friedgut. Shana Tova (= Happy New Jewish Year) to all our readers. The following is a real-life question. I recently rode my bike around a closed track. The track consists of a flat … Continue reading
Posted in Guest post, Sport, Test your intuition
Tagged Ehud Friedgut, Guest blogger, Test your intuition
4 Comments
Test your intuition 52: Can you predict the ratios of ones?
Here is a problem I heard from Zachary Chase and Yuval Peres. Bob choses a sequences of zeroes and ones of length . The bits are presented to Alice one by one. Alice’s task is to choose, at a certain … Continue reading
Some News from a Seminar in Cambridge
On an old problems of Erdős (h/t Michael Simkin and Nati Linial) Here is a somewhat mysterious announcement for a combinatorics seminar lecture at Cambridge. Which old problems of Erdős are we talking about? Here is a picture from the … Continue reading
Posted in Combinatorics, Test your intuition
Tagged Julian Sahasrabudhe, Marcelo Campos, Paul Erdos, Rob Morris, Simon Griffiths
16 Comments
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 average volume of a … Continue reading
Posted in Convexity, Geometry, Probability, Test your intuition
Tagged Test your intuition
12 Comments
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 … Continue reading
Test Your Intuition 50. Two-Player Random Walk; Can You Detect Who Did Not Follow the Rules?
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 according to the outcome. Their … Continue reading
Ehud Friedgut: How many cubes of 2×2×2 fit into a box of size 8×4×3? (TYI 49)
This blog post is kindly written by Ehud Friedgut. My daughter, Shiri, who’s in seventh grade, had the following question in a math exam: How many cubes of 2×2×2 fit into a box of size 8×4×3? Shiri divided the volumes, … Continue reading
Posted in Geometry, Riddles, Test your intuition
Tagged Alef's corner, Ehud Friedgut, Shiri Friedgut, Test your intuition
6 Comments
Combinatorics and more 