Category Archives: Test your intuition

TYI38 Lior Kalai: Monty Hall Meets Survivor

For breaking news, scroll down. Lior Kalai: Survivor Meets the Monty Hall Puzzle We start with the classical question and go on with a new version contributed by my son Lior. Update: A few brief comments on the original problem … Continue reading

Posted in Probability, Riddles, Test your intuition | Tagged , , , | 2 Comments

Test Your Intuition (or simply guess) 37: Arithmetic Progressions for Brownian Motion in Space

  Consider a Brownian motion in three dimensional space. What is the largest number of points on the path described by the motion which form an arithmetic progression? (Namely, , so that all are equal.)   A 2-D picture; In … Continue reading

Posted in Probability, Test your intuition | Tagged , | 8 Comments

Test Your Intuition (or knowledge, or programming skills) 36

How much is   The product ranges over all primes. In other words, Just heard it from Avinoam Mann.  

Posted in Number theory, Test your intuition | Tagged | 12 Comments

Test Your Intuition 35: What is the Limiting Distance?

(Just heard it today from Sergiu Hart.) At time t=0, point A is at the origin (0,0) and point B is distance 1 appart at (0,1). A moves to the right (on the x-axis) with velocity 1  and B moves … Continue reading

Posted in Test your intuition | Tagged , | 18 Comments

Testing *My* Intuition (34): Tiling High Dimension with an Arbitrary Low-Dimensional Tile.

Test your intuition 34 asked the following: A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If   can be partitioned into copies of we say that tiles . Here … Continue reading

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Test Your Intuition (34): Tiling high dimensional spaces with two-dimensional tiles.

A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If   can be partitioned into copies of we say that tiles . Here is a simpe example. Let consists of … Continue reading

Posted in Combinatorics, Test your intuition | Tagged | 7 Comments

Test your intuition 33: Why is the density of any packing of unit balls decay exponentially with the dimension?

Test your intuition: What is the simplest explanation you can give to the fact that the density of every packing of unit balls in is exponentially small in ? Answers are most welcome. Of course, understanding the asymptotic behavior of … Continue reading

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 4 Comments

Stan Wagon, TYI 32: Ladies and Gentlemen: The Answer

TYI 32, kindly offered by Stan Wagon asked A round cake has icing on the top but not the bottom. Cut out a piece in the usual shape (a sector of a circle with vertex at the center), remove it, … Continue reading

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 8 Comments

Ladies and Gentlemen, Stan Wagon: TYI 32 – A Cake Problem.

The following post was kindly contributed by Stan Wagon. Stan (Wikipedea) is famous for his books, papers, snow-sculptures, and square-wheels bicycles (see picture below) !     A round cake has icing on the top but not the bottom. Cut out a … Continue reading

Posted in Combinatorics, Guest blogger, Test your intuition | Tagged , , | 8 Comments

TYI 31 – Rados Radoicic’s Rope Problem

  Ropemaker (source) Rados Radoicic wrote me: “Several years back, I heard the following puzzle that turns out to be rather ‘classical’: “There are N ropes in a bag. In each step, two rope ends are picked uniformly at random, tied … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged , | 7 Comments