I draw numbers 1 through k (k≤10) out of a hat ten times at random, replacing the numbers after drawing them. If I disregard the case where I draw "1" all ten times, explain why the number of possible sequences is divisible by 11. (Result by a calculator is insufficient because anyone can do that easily.)

Now if I change the number '10' to another integer n in the above paragraph, can I still have a similar result; i.e., the total possible number of configurations is divisible by n+1? Does this work for all integers n? If so, prove it; if not, find all integers n it works for.

(In reply to re(3): Replace '10' by n by Richard)

I don't see how you get from the problem statement that n+1 must divide k^n-1 for all k=1,2,...,n. I only see that n+1 must divide n^n-1.

Posted by Bractals on 2006-09-05 00:32:58