You have some marbles in six colours: red, orange, yellow, green, blue, and violet. Each marble is one colour. Given the clues following, how many of each colour do you have?

1) The number of green marbles plus the number of violet marbles equals the number of blue marbles.

2) Of all of the pairs of marble colours, only orange and green total ten marbles.

3) There are more orange marbles and more yellow marbles each than there are red marbles.

4) The number of each of the red, orange, and yellow marbles are all primes and the number of each of the green, blue, and violet marbles are all not primes, unless it is the other way around.

5) The number of red marbles can be evenly divided by the number of blue marbles.

6) There are from one to nine marbles of each colour, and no two colours have the same number of marbles.

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, May 27, 2015 at noon Pacific Time.** I will post the answer shortly after.