The same colleague as in http://mathoverflow.net/questions/130489/another-colored-balls-puzzle asked me the following variant which she called "part II". Imagine you have $n$ ball …

I was sent this puzzle and wondered if it is known or if its origin is known? (I see colored ball puzzles are also in vogue.) Consider a bag with $n$ red balls and $n$ blue balls. …

As a member of boy scouts I was considering the following problem: suppose you're organising some kind of olympic games... *You divide the boys in $2n$ teams (subsets of equal size …

You're hanging out with a bunch of other mathematicians - you go out to dinner, you're on the train, you're at a department tea, et cetera. Someone says something like "A group of …

I’d like to verify if my formula correctly expresses that a number is a power of $ 10 $, using the $ \sf{TNT} $ language provided by Hofstadter in his famous book Gödel, Escher, Ba …

For pedagogical purposes I am looking for a function $\mathbb{N}\to\mathbb{N}$ that is defined everywhere but has most of its values unknown. Although such a function cannot be si …

The standard version of this puzzle is as follows: you have $1000$ bottles of wine, one of which is poisoned. You also have a supply of rats (say). You want to determine which bott …

The following identity is a bit isolated in the arithmetics of natural integers $$3^3+4^3+5^3=6^3.$$ Let $K_6$ be a cube whose side has length $6$. We view it as the union of $216$ …

Hello, I have the following conjecture: Write all numbers from $1$ to $n^2$ over an $n\times n$ board as usually. There not exists $n$ such that we can find a hamiltonian path on …

I was wondering this when using my bike lock, a combination lock with four dials, each of which has ten digits (0-9) on it in numerical order. Suppose a bicyclist decides that, fr …

Suppose you can make infinitely many copies of yourself. Each of them starts his/her life in a Hilberts Hotel, where each room is labeled by an element in the free group with two g …

On some occasion I was gifted a calendar. It displays a math quizz every day of the year. Not really exciting in general, but at least one of them let me raise a group-theoretic qu …

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no …

Please refer to this link for the puzzle: http://3.bp.blogspot.com/_jNRwOIxTW3U/S2mWv0uUKmI/AAAAAAAABK0/cFxX971MdV4/s1600-h/Thomas+Clausen+problem.png Thanks!

I need help with a problem about classic probability and possible extensions to it. Suppose you have an urn with $N$ distinguishable balls. Every time you draw $k$ balls out of $N$ …