Problem

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Tags: number theory, algebra



Six fruit baskets contain peaches, apples and pears. The number of peaches in each basket is equal to the total number of apples in the other baskets. The number of apples in each basket is equal to the total number of pears in the other baskets. (a) Find a way to place $31$ fruits in the baskets, satisfying the conditions of the statement. (b) Explain why the total number of fruits must always be multiple of $31$.