# Divide N items into M groups with as near equal size as possible

Im trying to split (say) N pink, fluffy balls into M groups as evenly as possible.

Eg: 9 Balls and 4 groups, i'd have a result set of the form: {3,2,2,2}, where each value is indicating the size of each subset.

Can anyone help me understand how to write an equation or algorithm that would solve this problem?

Thanks

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Well, you say "divide": so look at division: what information does it tell you? Can you use that to help solve the problem? – Hurkyl Sep 20 '12 at 13:09
Aside: you probably didn't mean "result set", because "set" is usually used to refer to a collection that doesn't count repetition: the sets {3,2,2,2} and {3,2} are the same. – Hurkyl Sep 20 '12 at 13:10
Ah yes, its flooding back to me now. cheers – Larry B Sep 20 '12 at 13:16

If you are given $N$ and $M,$ you put $\lfloor \frac NM \rfloor+1$ in $N \pmod M$ of the groups and $\lfloor \frac NM \rfloor$ in the rest.