Competition problem — Combinatorics

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Combinatorics Difficulty 5.2 AIME, harder Find the answer

6. There are four cows, each of which is either normal or mutated. A normal cow has 4 legs and always tells lies; a mutated cow either has 3 legs or 5 legs, and always tells the truth.

The owner asked the four cows: “How many legs do you have in total?”
The four cows answered: 13, 14, 15, 16.
So, these four cows have $\qquad$ legs in total.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

【Answer】 15

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.