Penny collects silver dollars. She's not sure how many dollars she has, but she knows it's fewer than 100.
When she puts them in piles of 2, 1 is left over.
When she puts them in piles of 3, 1 is left over.
When she puts them in piles of 4, 1 is left over.
When she put them in piles of 5, none were left over.
How many silver dollars did she have?
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Let N be the number of silver dollars Penny has.
Take one silver dollar away for a moment and consider the number N-1.
Then N-1 is multiple of 2, 3 and 4.
Hence, N-1 is multiple of 12.
It implies that N might be 13, 25, 37, 49, 61, 73, 85, 97, 109, . . .
From the other side, N must be multiple of 5 and it is less than 100.
Of these numbers, only N = 25 and N = 85 suit for these conditions.
Answer. Penny has either 25 or 85 silver dollars.