# Category Archives: Combinatorics

## Layish

This story is implicitly referred to in the 2008 opening post of this blog. ———– It was high time to raise the level of the discussion, I thought. Princeton, Fall 1995. We were a group of mathematicians at the IAS … Continue reading

## Some Mathematical Puzzles that I encountered during my career

Recently, I gave some lectures based on a general-audience personal tour across four (plus one) mathematical puzzles that I encountered during my career. Here is a paper based on these lectures which is meant for a very wide audience (in … Continue reading

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TYI 30 asked Elchanan Mossel’s Amazing Dice Paradox (that I heard from Yuval Peres yesterday) You throw a die until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws … Continue reading

## TYI 30: Expected number of Dice throws

Test your intuition: You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers. follow-up post

Posted in Combinatorics, Probability, Test your intuition | Tagged | 37 Comments

## Test your intuition 29: Diameter of various random trees

Both trees in general and random trees in particular are wonderful objects. And there is nothing more appropriate to celebrate Russ Lyons great birthday conference “Elegance in Probability” (taking place now in Tel Aviv) than to test your intuition, dear … Continue reading

## Micha Perles’ Geometric Proof of the Erdos-Sos Conjecture for Caterpillars

A geometric graph is a set of points in the plane (vertices) and a set of line segments between certain pairs of points (edges). A geometric graph is simple if the intersection of  two edges is empty or a vertex … Continue reading

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## Touching Simplices and Polytopes: Perles’ argument

Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection)   The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading

## Where were we?

I was slow blogging, and catching up won’t be so easy. Of course, this brings me back to the question of what I should blog about. Ideally, I should tell you about mathematical things I heard about. The problem is … Continue reading

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## Problems for Imre Bárány’s Birthday!

On June 18-23 2017 we will celebrate in Budapest the 70th birthday of Imre Bárány. Here is the webpage of the conference. For the occasion I wrote a short paper with problems in discrete geometry, mainly around Helly’s and … Continue reading