# Math

An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her 17 great-great-grandchildren, there would be 3 cards left over. If she divided her cards among her 16 great-grandchildren, there would be 10 cards left over. If she divided her cards among her 11 grandchildren, there would be 4 cards left over. If she divided her cards among her 7 children, there would be no cards left over.

What is the smallest possible number of cards in her collection?

A calculator may be helpful for this problem.

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1. The number of cards in her collection is divisible by 7.
The number of cards in her collection must also be even - consider the 16 great-grandchildren, with x being the number of cards each child would receive. The number of cards in the collection equals 16x +10, or 2(8x+5), indicating that it is divisible by 2.
Thus, the number of cards in her collection is divisible by 7x2 = 14
At this point, you could begin investigating multiples of 14, to see when you first find one that yields 3 integer answers for the 3 cases. This could be done with a calculator, or more quickly with an Excel spreadsheet.

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