Change the objective so that instead of having to get all 100 right, you only need the first 2 to get it right. This is more likely (given that in order to get all 100 right, the first 2 also have to get theirs right). Assume wlog that person 1 picks boxes 1 – 50. Person 2 can assume person 1 got his right, since otherwise they have lost already.. The best he can do is pick the other boxes 51 -100 (since he can assume one of the 1st 50 contained the other guy’s name: not his own). But this only gives him a 50/99 chance of getting his name!

Soooo, it seems to me the best you can do even for the first 2 people both being correct is only 25.25%!

I’ll see if I can find the error of my ways, but I ain’t seeing it.

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