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2013/14 AHSMC Part 1 Problem 6

Problem 6 of 16

Each of four cows is either normal or mutant. A normal cow has 44 legs and always lies. A mutant cow has either 33 or 55 legs and always tells the truth. When asked how many legs they have among them, their respective responses are 1313, 1414, 1515 and 1616. The total number of legs among these four cows is

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Solution

Since all four responses are different, at least three of them are wrong. If all four are wrong, then the cows are all normal, and they will have 1616 legs among them. However, this makes one of the responses right. Hence one of the responses is indeed right. The three normal cows have 1212 legs among them. Hence the mutant cow must have 33 legs in order to make one of the responses right. The answer is (C).

University of Alberta