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- New webpage at www.vadimkulikov.org March 24, 2017
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# Monthly Archives: December 2009

## Happy Transition 2009-2010!

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

Posted in Mathematics, Wednesday Problem
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## 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

Posted in Book & Article Reviews, Ramsey Theory
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## 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

Posted in Mathematics, Recreation, Wednesday Problem
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## 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:

Posted in Combinatorics, Games, Mathematics, Recreation
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## A Pizza Pun

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

Posted in Mathematics
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## 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, [tex]x_1,\dots,x_n\in \mathbb{R}^2[/tex]. What is the probability that the sum of these vectors has magnitude less than or equal to one, [tex]|x_1+\cdots+x_n|\leqslant 1[/tex]? (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

Posted in Book & Article Reviews, Education
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## 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

Posted in Mathematics, Recreation, Wednesday Problem
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## The Monkey and the Balls

I heard this story here at Mittag-Leffler institute from someone who heard it from someone else, who probably also heard it from someone else. (And so on.) What is the probability that I heard it from someone else? Just kidding. … Continue reading

Posted in Mathematics, Philosophy, Probability
2 Comments

## The Chocolate Game

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 [tex]n\times m[/tex] bar of chocolate on … Continue reading

Posted in Combinatorics, Games, Mathematics, Recreation, Wednesday Problem
2 Comments