# algebra

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Four boys sit down to play a game of marbles. They empty the bag of marbles and divide the marbles among themselves, and they find they have one marble left. A fifth boy comes along and wants to play, so they divide the marbles among all five boys and once again find that there is one marble left. A girl comes along and wants to play, so they divide the marbles among all six children and once again find that there is one marble left. What is the least number of marbles that were in the bag?

• algebra -

numbers divisible by 4 with one remainder:
5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 ...
numbers divisible by 5 with one remainder:
6 11 16 21 26 31 36 41 46 51 56 61 66 ..
numbers divisible by 6 with one remainder:
7 13 19 25 31 37 43 49 55 61 67 ...

looks like 61 is the smallest number common to all 3 sets

so there were 61 marbles.

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