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Results tagged with puzzle
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user 1061
Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.
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 …
- 6,711
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.
- 6,711
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 $1/2$ ( …
- 6,711
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 …