## Task A-1.3.

Dino, Pino, and Tino go to the same kindergarten. For the game, each boy needs two dice of the same color, but it is not necessary that the dice of different boys be of different colors. The caregiver has red, blue, and green dice in one box. If she draws without looking, how many dice does she need to draw from the box to be sure that each boy can take two dice of the same color?
## First Solution.

Two dice of the same color form a pair. Therefore, for each color, the caregiver draws some number of pairs and at most one additional die. If the caregiver were to draw dice among which there are no three pairs, the number of pairs could be at most two, and with those two pairs, there could be at most one die of each color. Thus, the maximum number of dice among which there are no three pairs is 7. This means that if the caregiver draws 8 dice, there will certainly be three pairs among them.

Furthermore, if the caregiver draws 7 or fewer dice, it is possible that there will not be three pairs. For example, she could draw 3 red, 3 blue, and 1 green die.

Therefore, the answer is 8.

Note: This way of thinking shows that if the number of children is $n$ and the number of colors is $k$, it would be necessary to draw $2(n-1)+k+1$ dice to ensure that each child can take a pair of dice of the same color.

Note: The answer alone, i.e., the result without justification, is worth 0 points. The proof that for eight dice, we can certainly find three pairs is worth 4 points. An example where for seven dice, we cannot find three pairs is worth 2 points.

It is necessary to provide an example of 7 dice among which there are no three pairs of the same color. Another such example is five dice of one color, and one die of each of the other two colors.