1. The box contains 10 red and 10 blue balloons. The seller, without looking, takes out one ball at a time. How many balls must be pulled out so that among the balls taken out of the box there will definitely be two balls of the same color?

2. How many pencils must be taken in the dark from a box with seven red and five blue pencils so that at least two red and at least three blue ones are taken?

3. Three types of candies, indistinguishable to the touch, were mixed in the bag. What is the smallest number of candies that must be taken at random from the bag so that among the taken candies there must be at least a) two; b) three of the same variety?

4. How many pencils can you take in the dark from a box in which there are 10 red, 8 blue, 8 green and 4 yellow pencils, so that there are obviously left in the box: a) at least 6 blue pencils; b) at least one pencil of each color; c) no more than 6 blue pencils?

5. There are 28 red, 20 green, 12 yellow, 20 blue, 10 white and 10 black balls in a box. How many balls must be pulled out without looking into the box so that among the pulled out balls there must be at least 15 balls of the same color?

6. In a dark closet there are boots lying in disarray: 10 pairs of black and 10 pairs of brown. How many shoes must be taken so that among them there is at least one pair (left and right shoe) of the same color? (In the dark, it is impossible to distinguish not only the color of the shoe, but also the left from the right.)

7. 6 people wearing galoshes of different sizes came to visit. They dispersed one by one, and some put on larger galoshes. How many guests could remain who were unable to put on their galoshes?

8. Winnie the Pooh, Piglet, Rabbit and Eeyore ate 70 bananas together, and each got some. Winnie the Pooh ate more than each of the others, and Rabbit and Piglet ate 45 bananas together. How many bananas did the donkey get?

9. There are 8 jars of strawberry jam, 7 raspberry jam and 5 cherry jam in the cellar. How many jars can you take out of the cellar in the dark with confidence that at least 4 jars of one type of jam and 3 jars of another will remain there?

10. What is the minimum number of chips that must be taken so that no matter how they are placed on the squares of the chessboard, there will definitely be 4 chips standing next to each other horizontally?

11. Several boxes together weigh 10 tons, with each box weighing no more than 1 ton. What is the smallest number of three-ton trucks that is known to be sufficient to carry the entire cargo?