Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
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Bad Things in Threes? It Doesn't Add Up
Three Puzzles Involving Number Three Building on this triplebolic mood, I'll end this section by mentioning three puzzles involving the number three. They are among the oddly many such three-puzzles. One is the Monty Hall 3 door problem, which I discussed in an earlier Who's Counting column. The second is the 3 hat problem, which I also described in another earlier column. And the third is the following: Approximately what percent of positive whole numbers contain the digit 3…