|Spoiler Inside: Solution to Puzzle||SelectShow>|
Let r, o, y, g, b, and v be the number of marbles of each colour.
By clue 4, b < g < o < r < v < y.
By clues 5 and 6, r can be 23, 29, or 31. Anything else will result in r + v + y > 99 (a violation of clue 6). By clue 2, o = r – 1. When o + r + v + y is considered, r must be 23. Thus, o = 22.
Let us make the other values as low as possible. Assuming this, v = 24, y = 25, and b = 1.
Applying clue 1, g must be 4. This gives a total of 99 marbles. Any other values chosen in the previous paragraph would result in more than 99 marbles.
The solution is r = 23, o = 22, y = 25, g = 4, b = 1, v = 24.