Question 15
Three fair dice, whose colours are red, yellow and blue, each with faces numbered from 1 through 6, are all thrown at the same time. How many different outcomes are there where the 3 dice rolls sum to a perfect square?
Note: Dice with the same numbers but have different colours are considered distinct outcomes. For example, (1, 2, 3) and (2, 3, 1) are different outcomes, where the ordered triple $(r,y,b)$ represents the numbers appearing on top of the red, yellow and blue dice, respectively.
Note: Dice with the same numbers but have different colours are considered distinct outcomes. For example, (1, 2, 3) and (2, 3, 1) are different outcomes, where the ordered triple $(r,y,b)$ represents the numbers appearing on top of the red, yellow and blue dice, respectively.