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divisible by 11? (Posted on 2006-09-04) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Bon    
Rating: 3.5000 (2 votes)

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Hints/Tips I'm not telling... | Comment 5 of 17 |
...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 2006-09-04 12:50:18
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