Asked by LoLa HeRMaN

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.
Answered by Motorhead
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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