Honza has a box of pastels in the attic of his cottage, containing 5 blue, 9 red, 6 green, and 4 yellow pastels. It is dark, the light in the attic is not working, and Honza does not have any source of light with him. Therefore, he cannot distinguish the colors of the pastels.

a) How many pastels does he need to take at minimum to be sure that he brings at least one pastel of each color?

b) How many pastels can he take at maximum to be sure that at least one pastel of each color remains in the box?

c) How many pastels can he take at maximum to be sure that at least five red pastels remain in the box?

(M. Volfová)
Let's always consider the least favorable situation:

a) If Honza took all the pastel colors except one, this color would still be missing. The least favorable situation occurs when yellow is missing, as there are the fewest of these pastels. The total number of all blue, red, and green pastels is $9+6+5=20$, so Honza must take at least 21 pastels.

b) If Honza took all the pastels of one color, this color would then be missing from the box. The least favorable situation occurs when he picks only yellow ones, as there are the fewest of these. There are 4 yellow pastels, so Honza can take at most 3 pastels.

c) The least favorable situation occurs when Honza takes only red pastels. There are a total of 9 of these, so he can take at most 4 pastels.

Suggested evaluation. 1 point for each correct answer; 3 points based on the quality of the explanation.