The box contained colored pencils: 10 red, eight green and blue, four yellow. In the dark we take pencils from the box.

The box contained colored pencils: 10 red, eight green and blue, four yellow. In the dark we take pencils from the box. What is the smallest number of pencils you need to take so that among them there are: a) at least four pencils of the same color; b) at least one pencil of each color; c) at least six blue?

a) You need to take at least 4 pencils of the same color.
3 red + 3 blue + 3 green + 3 yellow, it is enough to take 1 more pencil, then there will definitely be 4 pencils of the same color;
Answer: 3 * 4 + 1 = 13 pencils;

b) You need to take at least one pencil of each color.
10 red + 8 blue + 8 green, just take 1 more pencil, it will definitely be yellow.
Answer: 10 + 8 + 8 + 1 = 27 pencils;

c) You need to take at least six blue pencils.
10 red + 8 green + 4 yellow = 22 pencils, the next 6 will definitely be blue;
Answer: 22 + 6 = 28 pencils.