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.

(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