Easy math puzzles

Quote: Wizard

Here is something a bit easier.

How many ways are there to put six distinct balls into three identical boxes?

Is there a general formula for n distinct balls into three identical boxes?
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There are only seven partitions of six using 1-3 digits:

6
15
24
33
114
123
222

It's easy to calculate the number of combinations for any of them. For instance, there are combin(6,1) * combin(5,2) * combin(3,3) = 60 combinations of 123. The combinations of all seven partitions sum to the answer of 122 combinations for boxes containing 0-6 balls.

If all boxes must contain at least one ball, then we subtract the 32 combinations of 6, 15, 24 and 33 to get the answer of 90 combinations

Incidentally, regarding the “random board cuts” problem: You guys analyzed it for days, eventually concluding there was no direct solution for n cuts, then I post the direct solution using nothing but basic combinatorics/calculus, and apparently no one cares?