Enigma 1689: What’s my number?
14 March 2012
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From New Scientist #2856, 17th March 2012 [link]
Three very logical friends, Amy, Bob and Carol, sat in a circle wearing hats. Each hat had a number on it so all three could see the others’ numbers but not their own. They were told that the numbers were three different positive digits.
They each made a statement in turn and were told to raise their hands when they knew their own number. Amy said: “Carol’s number is greater than Bob’s.” No one raised their hand.
Bob then said: “The sum of Amy’s and Carol’s numbers is even.” On hearing this, Carol raised her hand. Even then Amy and Bob did not raise theirs. But, after a pause, and once it had become clear that Amy wasn’t going to raise her hand, Bob raised his and then Amy raised hers.
What were Amy’s, Bob’s and Carol’s numbers?