Question 186391
When John sorts his collection of computer card games into groups of 3, 4, 5 and 8 there is always one card left. What is the smallest number of cards John can have? 
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3 is divisible by 3; but 3+1 leaves a remainder of one when you divide by 3
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3*4 is divisible by 3, and it is divisible by 4; but 3*4+1 leaves a remainder
of 1 when you divide by 3 or when you divide by 4
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Similarly 3*4*5*8+1 will have a remainder of 1 when you divide by 3,or
4, or 5, or 8
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But the 4 and the 8 share a factor of 4, so we don't need the 4 as
a separate factor to achieve divisibility by 4.
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So the smallest number that satisfies the condition is
3*5*8+1 = 121
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Cheers,
Stan H.