Monthly Archives: January 2010

The Coin Placing Game.

See the Wednesday Problem’s vague rules here. Some games again. According to Sam, from whom I heard this riddle, it divides people into cathegories i) those who realize the answer immidiately and ii) those who think quite long about it. … Continue reading

Posted in Games, Recreation, Wednesday Problem | 6 Comments

TopoLogic

The Continuum Hypothesis trilogy will continue later. Today I’ll recall some discussion I made a year ago or so in the student seminar. I guess someone would say that it is surprising, how closely related these two branches of mathematics … Continue reading

Posted in Logic, Mathematics, Topology | 2 Comments

How Old Are The Kids?

Please comment your solutions, questions and remarks.. This is quite famous. But maybe you haven’t heard it yet: A math student goes to a party organized by her supervisor. The student asks: How many daughters do you have? And the … Continue reading

Posted in Combinatorics, Recreation, Wednesday Problem | 2 Comments

Continuum Hypothesis III

Suppose you pick randomly a real number. What is the probability that it equals to 1? The probability is zero. Suppose $$X\subset [0,1]$$ is a countable subset of the unit interval. What is the probability that a randomly picked real … Continue reading

The Monk

Please comment your solutions, questions and remarks.. The posts have been a bit advanced lately. Let us lighten the atmosphere by this riddle which admits a simple solution, though mathematicians tend to use calculus in solving it: An Indian monk … Continue reading

Posted in Calculus, Recreation, Wednesday Problem | 2 Comments

Continuum Hypothesis II

Differentiability of Space Filling Curves A Peano curve is a surjective (onto) function $$f\colon\mathbb{R}\to\mathbb{R}^2$$. Apparently such an f cannot be smooth. To see this consider the restrictions of this function to closed intervals $$f\restriction [n,n+1]$$. By smoothness and compactness the … Continue reading

White Math Days

We had literally white Mathematics Days in Jyväskylä. For more pictures

Posted in Meta | 2 Comments

Please comment your solutions, questions and remarks.. Maximal Almost Disjoint families. This is not so much of a riddle than just a theorem, but the solution is fun, so I would like to place it here. This is like a … Continue reading