Puzzle
A passer by gives you the following puzzle:
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If counted in pairs one remains
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If counted in threes,two will remain
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If counted in fours, three will remain
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If counted in fives, four will remain
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If counted in sixes, five will remain
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If counted in sevens, nothing will remain
If this number is lower than 150, what is it?
The answer is 119.
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1 solution
We can easily see that on adding 1 the number becomes divisible by 2,3,4,5 & 6. so the successor is divisible by 60. this means our number is either 59 or 119. (In general it is 60n-1). As we have only 2 numbers, just check the remainder with 7.