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!
Solution Stats
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers59
Suggested Problems
-
Sum all integers from 1 to 2^n
17890 Solvers
-
Project Euler: Problem 1, Multiples of 3 and 5
3715 Solvers
-
Return the first and last characters of a character array
12271 Solvers
-
Find third Side of a right triangle given hypotenuse and a side. No * - or other functions allowed
253 Solvers
-
Check that number is whole number
5431 Solvers
More from this Author80
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
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.
http://oeis.org/A000166