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Cindy has a pile of $1 coins. when she stacks them into groups of two, there is one coin left over.
When the stacks them into piles of three, there is one coin left over,
and when she stacks them into groups of five there is one left over.
What is the smallest number of $1 coins that Cindy has in her bag ?
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Answer. 2*3*5+1 = 31.
Solution
Let N be the unknown number under the question.
Consider the number N-1.
It is divisible by 2, by 3 and by 5, according to the condition.
The minimal such a number is 30 among the whole numbers.
Hence, yours number is 30 + 1 = 31.
