Yet another marbles problem! You have some marbles which are each of one colour of red, orange, yellow, green, blue, and violet. From the clues below, determine how many marbles of each colour you have.
- The total number of orange marbles and green marbles is equal to the number of yellow marbles.
- Three of the colours have an even number of marbles; the same for odd.
- The numbers of yellow and violet marbles are both even or both odd.
- There are at least two of each marble colour, but no more than nine.
- The numbers of red and blue marbles are both even or both odd.
- There is a different number of each of the six colours.
- From lowest to highest numbers of marbles is the same order as the colours in ascending alphabetical order.
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, October 2, 2013 at noon Pacific Time. I will post the answer shortly after.