(2) If only four students can solve each problem, then the conclusion of (1) is generally not valid. Try to construct an example to illustrate this point.
2. The dial of the clock is marked with numbers 1, 2, 3, …, 1 1, 12 in a standard way, and there are any n sectors on it, each sector covers exactly 4 numbers, and every two covered numbers are different. If you don't start here,
There are four multiple-choice questions on the test paper, and each question has three alternative answers. A group of students took part in the test, and the result was that any three of them had different answers to a question. How many students will take the exam at most?
4. Six children each have at least 1 book, and one * * * has 20 books. Try to prove that at least two children have the same number of books.
There are 40 students in the class with less than 780 books. Prove that at least two students have the same number of books.
6. There are 5050 digital cards, of which 1 means 1, 2 means 2, 3 means 3... 100 means 100. Now, how many cards should I draw? How many cards should be drawn to ensure that at least 10 cards are the same?
7. There are 10 beads of different colors in the pocket, each of which is 100. How many beads do you have to take out of your bag to ensure that there are at least 10 beads of three different colors?
8. Each of the two bags has 12 small balls of the same size, four in red, four in white and four in blue. Take as few balls as possible from the first bag, but put at least two colors in the second bag; Then take as few balls as possible from the second bag and put them in the first bag, so that there are not less than three balls of each color in the first bag. How many balls are there in each bag at this time?
9. Transport several boxes of goods weighing 19.63 tons by vehicles with a load of10.5 tons. The weight of each box of goods is the same, not exceeding 350 kg. When the weight of each box of goods is heavy, you need the most cars? How many cars do you need at most?
10. The height (in whole centimeters) of fifth-grade students in a primary school is the shortest 138 cm and the highest 160 cm. If several students are randomly selected from these students, how many students must be selected at least to ensure that five people are the same height?
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