Puzzle #18: Kittens!

Oh, look! A box full of kittens. There are twelve of the beauties. All of them are at least one colour of black, white, and orange. Given the following clues, how many are there of each of the colour combinations?

  1. There is a different number of each of the combinations containing black.
  2. There are six one-colour kittens.
  3. There is a different number of each of the multi-colour combinations.
  4. No kittens are coloured only black and orange.
  5. There is a different number of each of the one-colour combinations.
  6. There are four kittens coloured orange and white and maybe black.
  7. There is a different number of each of the combinations containing orange.
  8. Six of the kittens are black, seven are white, and six are orange.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, October 9, 2013 at noon Pacific Time. I will post the answer shortly after.