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Arrange the Fruits

A shopkeeper arranges his fruits in such a way that putting either 3,or 9,or 7 apples in a row, each time one apple is left out. But when he puts 11 apples in a row, number apple is left. Find the number of apples.

SOLUTION : By given information, the number of apples is 1 more than a multiple of 3, 9 and 7 and an exact multiple of 11. The smallest number that is 1 more than a multiple of 3, 9 and 7 is 64. But, it is not a multiple of 11. The next such numbers are 127, 190, 253, 316, 379, and so on. The smallest among these which is a multiple of 11 is 253. So, the number of apples is 253.

However, there can be multiple answers. 946 is another answer that satisfies all constraints. In fact, any number of the form 253+ 693n is an answer, where n is a whole number. But, if asked for smallest answer, 253 is the answer.

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