This question on MathOverflow discusses the problem of finding the distribution of the maximum value of a multinomially-distributed random variable: https://mathoverflow.net/questions/104948/distribution-of-maximum-of-a-uniform-multinomial-distribution
Using the formula on that page, and the bounds on test set 1, I get an upper bound of P(max >= 18) <= 0.8131. This drastically overestimates the actual probability, but it's still significantly less than 1. So we can perform multiple trials, and reduce the probability of getting incorrect results on _all_ of them to a very small number. (With 365 trials, the chance of error is at most 0.8131^365 ~= 10^-33.) -- David -- You received this message because you are subscribed to the Google Groups "Google Code Jam" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/google-code/1f493340-59e0-434c-96dc-f893ae63fd01%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
