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October 20th, 2017, 02:12 PM   #1
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Unhappy Combinatorics with several conditions

Hello. I have a math problem that I need to solve, however I'm really stuck and also kind of depressed now.

We have 30 balls. 6 red, 7 white, 9 green and 8 blue. We want to separate them to 4 different boxes.
• First box can only contain 13 or less balls, which can be either red or white. Number of red and white balls in this box must be equal.
• Second box can contain 13 or less balls, which can be either green or blue. There must be at least one ball from each of these colors.
• Third box can contain 10 or less balls, which can be either blue or red. However there can only be be balls from one of these colors. Not both.
• Fourth box can contain 8 or less balls, which can be either white or green. This box can’t stay empty.

If the condition doesn’t say otherwise, boxes can remain empty as well.

I've tried several ways, but always get confused by different conditions. I have best luck with inclusion-exclusion principle, but still it was too difficult to solve. Can you please help me?

Last edited by skipjack; October 21st, 2017 at 03:19 AM.
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