BobbyGo

If I'm reading this right...

Oh wow, I was horribly off. (It would have helped to read the OP a bit more thoroughly)

Sorry, had trouble with the spoilers.

If the common denominator for the first six probabilities is 66, why does the equation for P7 have a denominator of 67? Shouldn't the equation be: P7 = (65 + 7*64 + 72*63 + 73*62 + 74*6 + 75)/ 66 (Which equals my attempted answer of about .2536043952903521) If this is right, I would assume that the common denominator would cap at 66 as, eventually, all probabilities would be averages of probabilities with a 66 denominator; including P137. The disproof stands. I speculated, Bushindo's code could be something similar to the inductive step in my disproof. This problem runs deeper than it appeared at the first glance. However, our tag team solution is practical. It must be exact for any intermediate sum past infinity. And 137, as it turns out, is a hefty step towards the infinity. I see where I went wrong. Somehow, I thought you were dividing the sum of the numerators by 6 and multiplying the denominator by 6. When I did mine, I worked the numerators first and then divided by the denominator to get a decimal number; opposed to your cleaner method of just multiplying the denominator and leaving it in fractal form. If that makes any sense whatsoever. I'm at work and it's hard to concentrate. (That's my excuse and I'm sticking to it)

I'm glad I wasn't too far off in my thinking. I had a similar approach, but only considered 131 - 136 when trying to calculate the odds for 137. I had wrongly assumed each number 131 - 136 would have an equal likelyhood of being hit irrespective of of the likelyhood of any of the previous numbers. I do have a question about one part of your disproof: If the common denominator for the first six probabilities is 66, why does the equation for P7 have a denominator of 67? Shouldn't the equation be: P7 = (65 + 7*64 + 72*63 + 73*62 + 74*6 + 75)/ 66 (Which equals my attempted answer of about .2536043952903521) If this is right, I would assume that the common denominator would cap at 66 as, eventually, all probabilities would be averages of probabilities with a 66 denominator; including P137.

Can the mother be alone with a son on the boat? and vice versa? And can the criminal be by himself without the cop? Or will he run off?