What’s my number?
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?
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WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 18 April. The Editor’s decision is final. Please send entries to Enigma 1689, Â鶹´«Ã½, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
Answer to 1680 Do magic: (a) 34; (b) 1398
The winner David Porter of Norton, County Durham, UK
Answer to 1683 Lottery numbers: The balls in order are 20, 31, 02, 03 and 10
The winner Karen Shefford of Arkesden, Essex, UK
