What鈥檚 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鈥� 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: 鈥淐arol鈥檚 number is greater than Bob鈥檚.鈥� No one raised their hand.
Bob then said: 鈥淭he sum of Amy鈥檚 and Carol鈥檚 numbers is even.鈥� 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鈥檛 going to raise her hand, Bob raised his and then Amy raised hers.
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What were Amy鈥檚, Bob鈥檚 and Carol鈥檚 numbers?
WIN 拢15 will be awarded to the sender of the first correct answer opened on Wednesday 18 April. The Editor鈥檚 decision is final. Please send entries to Enigma 1689, 快猫短视频, Lacon House, 84 Theobald鈥檚 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