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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.

6 votes

Another colored balls puzzle (part II)

As Douglas Zare points out in a comment to Vincent Beffara's answer, in case 1 the expected time to completion of the process, starting from $(1,n-1)$ is $2^n-1$. To see this, consider a simple random …
Ori Gurel-Gurevich's user avatar
18 votes
Accepted

How to get rich in a Hilberts Hotel?

No, you cannot get rich with identical copies on the unlabeled tree. This is a special case of the Mass Transport Principle - take a look at the book of Lyons and Peres, chapter 8.
Ori Gurel-Gurevich's user avatar
17 votes

Identifying poisoned wines

You yourself give the solution in the link: the probabilistic method. Without trying to optimize, take $r$ rats and for each one choose the subset of wines randomly, each wine with probability $1/2$ ( …
Ori Gurel-Gurevich's user avatar
30 votes
Accepted

A balls-and-colours problem

It can probably be done by looking at the sum of squares of sizes of color clusters and then constructing an appropriate martingale. But here's a somewhat elegant solution: reverse the time! Let's fo …
Aaron Meyerowitz's user avatar