## Task 2 - 290522

Susanne owns 18 dice. Some of them are red, others are blue, and the rest are yellow. She notices that the number of blue dice is 1 less than twice the number of red dice. Furthermore, she observes that if you increase the triple of the number of red dice by 1, it equals the number of yellow dice.

Show that Susanne's observations can only be true for one specific combination of the three numbers of red, blue, and yellow dice! Provide these three numbers!
If $x$ is the number of red cubes, then according to Susanne's observations, $2 x-1$ is the number of blue cubes and $3 x+1$ is the number of yellow cubes.

The sum of the three quantities is 18, so it follows

$$
x+2 x-1+3 x+1=18 \quad ; \quad x=3
$$

From this, it follows further that $2 x-1=2 \cdot 3-1=5$ and $3 x+1=3 \cdot 3+1=10$.

Therefore, Susanne's observations can only be true if the number of red cubes is 3, the number of blue cubes is 5, and the number of yellow cubes is 10.