1. Draw two trump cards from playing cards, and randomly draw five cards from the remaining 52 cards, at least two of which are of the same suit. Try it and explain why.

There are ***4 colors, according to the principle of pigeon's nest: 5 cards are put into 4 drawers, and there must be 2 cards in one drawer.

2. Uncle Zhang participated in the darts competition and threw five darts, with a score of 4 1. Uncle Zhang has at least one dart and not less than nine. Why?

According to the pigeon hole principle: put 4 1 ring into five drawers, at least one drawer has 9 rings.

3. Mix 10 red, blue and yellow. If you close your eyes, how many sticks can you take out at least once to ensure that there are two sticks of the same color?

It will bring bad luck to smoke three red, blue and yellow sticks. At this time, you can draw another one at will to ensure that there will be two sticks of the same color.

Namely: 3+ 1=4.

4. Draw six faces of a cube in blue and yellow respectively. No matter how you draw it, at least three faces are the same color. Why?

According to the pigeon hole principle, if six sides are put into two drawers, there must be 1 drawer with three sides.