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N dice (Posted on 2017-05-25) Difficulty: 3 of 5
In "5 dice" Andy had five regular dice. Now he has a total of N regular dice. He claims that the odds of rolling exactly M sixes is exactly half as likely as rolling (M-1) sixes. (M < N).

For what values of N is this true?

State the pattern if there is one.

Express M as a function of N.

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

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 2 of 3 |
(In reply to Solution by hoodat)

Very nice, hoodat.


It took me a while to figure out that your 2.5 factor was the fivefold increase in combinations times 1/2 (the desired ratio of probabilities).  Once I figured this out, all was well.

I checked out your first case, N = 6 and M = 2, and it had the desired 1/2 relative probability



  Posted by Steve Herman on 2017-05-25 12:12:41
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