- The sum of two blue numbers gives a green number.
- The sum of two green numbers gives a blue number.
- The rest of the numbers are red.
- The number one is green

**What color will be the numbers from 1 to 10?**

#### Solution

If the number one is green, the 1 + 1 = 2 must be blue, according to the second rule. Therefore, the 2 + 2 = 4 must be green, according to the first rule, and the 1 + 4 = 5 must be blue. Reasoning analogously, 7 must be green, 8 blue and 10 green.

The rest of the numbers: 3, 6, and 9 must be red, because if 3 were green, 3 + 1 = 4 must be blue, not green, and that would go into contradiction. In the same way, 6 + 1 = 7 is green, and that is why 6 cannot be green, and 10 is green, so 9 cannot be green either. But they can't be blue either, since 2 is blue, and 3 + 2 = 5 is blue, just like 8 and 11. That's why 3, 6 and 9 are red.