Bags of gems

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Here is another one I found in Smullian's book.


You have ten bags of gems. Each bag contains three gems, which are either diamonds, rubies, or emeralds. As it happens, no two of the ten bags have exactly the same combination of these gems. For instance, one bag contains three diamonds, another contains two rubies and an emerald, another contains one of each.

You reach into one of the bags, and happen to pull out a diamond. You are now allowed to pull one stone out of any of the ten bags. If that second stone is also a diamond, you get to keep it. Otherwise, you get nothing. Are you better off taking the second stone from the bag you first pulled the diamond out of, or out of one of the other nine bags?


The Riddle of Scheherazade: And Other Amazing Puzzles by Raymond Smullyan.