You have an equal number of cups and balls, each labelled from one to N. You randomly place one ball in each cup. Determine the number of possible combinations such that no balls are in the cup with a matching number. For example, if you have three balls and three cups, there are two valid solutions:
- 2, 3, 1
- 3, 1, 2
The following permutations do not meet the criteria for the reasons listed:
- 1, 2, 3 (all three balls are in the correct cups)
- 1, 3, 2 (ball 1 is in cup 1)
- 3, 2, 1 (ball 2 is in cup 2)
- 2, 1, 3 (ball 3 is in cup 3)
Good luck!
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Problem Comments
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2 Comments
Jean-Marie Sainthillier
on 8 Apr 2013
I think that with this kind of problem, you can process in two steps.
A first easy problem with small N (to test perms for example). And a harder problem with big N, which
oblige to find another algorithm.
Binbin Qi
on 27 Oct 2014
http://oeis.org/A000166
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