Oh, look! A box full of kittens. Everything is cuter with kittens. There are 24 of the darlings. They come in three colours. 17 are black, 16 are grey, and 12 are white. Obviously, there is some overlap. For this puzzle, black is a colour. (You would not want to hurt a black kitten’s feelings, would you?)
Solve these scenarios:
1) What is the maximum possible number of kittens having one colour only? (i.e. Maximise just black + just grey + just white.)
2) Like #1, but there must also be at least three one-colour kittens of each colour.
3) What is the maximum possible number of three-colour kittens?
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 14, 2014 at noon Pacific Time. I will post the answer shortly after.