The positive integers have been coloured red, blue or green: 1 is red, 2 is blue, 3 is green, 4 is red, 5 is blue, 6 is green, and so on. Renate calculates the sum of a red number and a blue number. What colour can the resulting number be?impossible to sayred or blueonly greenonly redonly blue

The pattern of the colors follows a cycle of three: red, blue, green. This means that the color of any positive integer can be determined by its remainder when divided by 3.

1. Red numbers are those that leave a remainder of 1 when divided by 3 (1, 4, 7, 10, etc.).
2. Blue numbers are those that leave a remainder of 2 when divided by 3 (2, 5, 8, 11, etc.).
3. Green numbers are those that leave a remainder of 0 when divided by 3 (3, 6, 9, 12, etc.).

When Renate calculates the sum of a red number and a blue number, we can think of it as adding a number with a remainder of 1 (red) and a number with a remainder of 2 (blue) when divided by 3.

1 (remainder when red number is divided by 3) + 2 (remainder when blue number is divided by 3) = 3

A number that leaves a remainder of 3 when divided by 3 is actually a multiple of 3, and therefore, it is green.

So, the resulting number can only be green.