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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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/TipsNot solved yet - Hintsvswitchs2006-09-06 13:36:00
re(7): Replace '10' by nRichard2006-09-06 02:55:58
re(6): Replace '10' by nBractals2006-09-05 10:16:00
re(5): Replace '10' by nRichard2006-09-05 01:24:36
Questionre(4): Replace '10' by nBractals2006-09-05 00:32:58
re(3): Replace '10' by nRichard2006-09-04 20:21:48
Some Thoughtsre(2): Replace '10' by nBractals2006-09-04 19:43:31
re: Replace '10' by nRichard2006-09-04 16:17:22
QuestionReplace '10' by nBractals2006-09-04 16:01:57
re: I'm not telling...JLo2006-09-04 14:09:26
re: almost solutionRichard2006-09-04 13:25:54
Hints/Tipsalmost solutionCharlie2006-09-04 12:53:59
Hints/TipsI'm not telling...vswitchs2006-09-04 12:50:18
Some more datavswitchs2006-09-04 12:32:06
No Subjectvswitchs2006-09-04 12:14:39
Insufficient, but a startRichard2006-09-04 11:14:29
Hints/TipsHint. Spoiler.Steve Herman2006-09-04 09:12:31
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