You have some marbles. Each is of one colour of red, orange, yellow, green, blue, and violet. You have one to nine of each colour with a different number of each colour. Given the following clues, how many of each colour do you have?
1) The number of red plus yellow plus violet equals the number of orange plus green plus blue.
2) The total of the number of red, orange, and yellow marbles is the same as the total of the number of marbles of some other colour.
3) The number of orange, green, and blue marbles are all odd.
4) There are fewer red marbles than any other colour.
5) There are two more blue marbles than green marbles.
6) There are more violet marbles than any other colour.
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 1, 2017 at noon Pacific Time. I will post the answer shortly after.