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.
...but I'll be having fun watching you.
I smelled something, looked it up, and I had smelled correctly  but I'm not giving it away this early.
Let's just say it is a theorem by a famous mathematician whose other main theorem was proven only recently.
But it is nothing nasty  it can actually be proven in an elementary fashion, without background knowledge and without writing pages of formulas. Have fun  I sure will.

Posted by vswitchs
on 20060904 12:50:18 