# Monthly Archives: December 2009

## Happy Transition 2009-2010!

Please comment your solutions, questions and remarks.. Which one is bigger: $$\sqrt{2009 + \sqrt{2010}} + \sqrt{2010 + \sqrt{2009}}$$ or $$\sqrt{2009 + \sqrt{2009}} + \sqrt{2010 + \sqrt{2010}}$$? (If you use a calculator, show that it does not lie) 2/5 … Continue reading

## My Brain Is Open, the mathematical journeys of Paul Erdös: A Book Review

During my stay at the Mittag-Leffler Institute I read this book written by Bruce Schechter. The book is written in accessible English, so that I had no problems reading it though English is not my mother tongue. It tells the … Continue reading

## Joulupukki Is Fair: Your Christmas Riddle

Please comment your solutions, questions and remarks.. Joulupukki came to a kindergarten. He had some number of candies to give to the children. He saw that there are more boys than girls and that he could divide the candies evenly … Continue reading

## The Game Discrete

Inspired by my post about tic-tac-toe I want to introduce a game. It is played on a 3x3x3 grid or equivalently on a 9×3 grid:

## A Pizza Pun

$$\textrm{Suppose we have a pizza with radius }z$$ $$\textrm{ and thickness }a\textrm{. Then the volume is}$$ $$\pi \cdot z \cdot z \cdot a.$$

## Handshaking Lemma

Please comment your solutions, questions and remarks.. This one I learned from Sam Hardwick. Show that the number of those, who have shaken their hands with others an odd number of times, is even. Level 1/5 P.S. This lemma has … Continue reading

Posted in Combinatorics, Recreation, Wednesday Problem | 2 Comments

## Where Do Random Walks Lead

Rami Luisto asked the following question: Pick randomly n unit vectors from the plane, $$x_1,\dots,x_n\in \mathbb{R}^2$$. What is the probability that the sum of these vectors has magnitude less than or equal to one, $$|x_1+\cdots+x_n|\leqslant 1$$? (magnitude = norm = … Continue reading

Posted in Calculus, Mathematics, Probability | 3 Comments

## Tips to Young Mathematicians

I read the article “Advice to a Young Mathematician” written by five authors Sir Michael Atiyah, Bela Bollobas, Alain Connes, Dusa McDuff and Peter Sarnak. In the following I summarize in eight clauses what I found useful and what was … Continue reading

## Ants

Please comment your solutions, questions and remarks.. This funny riddle I heard from Marcin Sabok. There are n ants on the unit interval, [0,1]. Each has a direction, left or right. In the picture above there are three ants and … Continue reading

Please comment your solutions, questions and remarks.. I heard this from Lauri Hella, but he doesn’t remember from whom he heard this. The game is played between two players as follows. There is an $$n\times m$$ bar of chocolate on … Continue reading