Solution: Four different colors can be regarded as four drawers with gloves as elements. Make sure one pair is the same color. 1 There are at least two gloves in the drawer. According to the pigeon hole principle, at least five gloves should be pulled out. At this time, take out 1 double color, and there are 3 gloves left in the last 4 drawers. According to the pigeon hole principle, as long as two gloves are pulled out, one glove can be guaranteed to be the same color, and so on.
Think of four colors as four drawers. To ensure that there are three pairs of the same color, first consider ensuring that there are 1 pair, and then you must pull out five gloves. At this time, after taking out 1 with the same color, there are still three gloves left in the four drawers. According to the pigeon hole principle, as long as two gloves are pulled out, it can be guaranteed that 1 pair is of the same color. By analogy, it is guaranteed that there are 3 pairs of the same color, and the gloves drawn out by * * * are: 5+2+2=9 (only)
Answer: At least 9 pairs of gloves must be drawn out to ensure that there are 3 pairs of gloves of the same color.
2. There are several building blocks with four colors, and each person can take 1-2 blocks at will. At least a few people can take them to ensure that three people can get exactly the same.
The answer is 2 1.
Solution:
There are four different ways for each person to take 1 piece, and there are six different ways for each person to take 2 pieces.
When there are 1 1 individuals, it can be guaranteed that at least two people will be exactly the same:
When there are 2 1 person, at least 3 people can be guaranteed to be exactly the same.
3. A box contains 50 balls, of which 10 is only red, 10 is only green, 10 is only yellow, 10 is only blue, and the rest are white balls and black balls. In order to ensure that the balls taken out contain at least 7 balls of the same color, Q: How many balls must be taken out of the bag at least?
Solution: It needs to be discussed in different situations, because it is impossible to determine the number of black balls and white balls.
When there is no black ball or white ball greater than or equal to 7, it is:
6*4+ 10+ 1=35 (pieces)
If there are seven black balls or white balls, that is:
6 * 5+3+ 1 = 34 (pieces)
If there are eight black balls or white balls, that is:
6*5+2+ 1=33
If there are nine black balls or white balls, that is:
6*5+ 1+ 1=32
4. There are four piles of stones on the ground, and the number of stones is 1, 9, 15 and 3 1 respectively. If 1 stone is taken out from three piles at the same time and then put into the fourth pile, after several calculations, can the number of stones in these four piles be the same? (If yes, please explain the specific operation; If not, please explain why. )
No
Because the total is1+9+15+31= 56.
56/4= 14
14 is an even number.
The original 1, 9, 15, 3 1 are all odd numbers, and taking out 1 and putting in 3 are also odd numbers. If you add and subtract odd numbers several times, the result must still be odd, and it is impossible to get even numbers (14).
1, a canal. On the first day, the full-length 1/3 was repaired, and the rest 1/3 was repaired the next day, leaving 300 meters to be repaired. How long is this canal?
2. Pour out 1/3 bottles of alcohol for the first time, then pour 40 grams back into the bottle, pour out 5/9 of the alcohol in the bottle for the second time, and pour out 180 grams for the third time, leaving 60 grams in the bottle. How many grams of alcohol are there in the bottle
3. Students in three classes of grade six in a school do math learning tools. Class 6 (1) accounts for 2/5 of the total number of class 3. Class 6 (2) is more than Class 6 (3) 1/4, and less than Class 6 (1) 10. How many learning tools did Class Six (2) make?
There are 248 workers in a factory, of whom 15/3 1 are women. Later, several women workers were transferred, so the number of women workers accounted for 7/ 15 of the total number. How many female workers have been transferred?
5. The library has *** 1880 literature books, science books and comic books, 2/5 literature books are lent out, 50 science books are lent out and 40 comic books are bought. At this time, the number of three types of books is the same. How many books are there in each of these three types?
Example 5: The edible oil in barrel A is 2.4 kilograms more than that in barrel B. If 0.6 kilograms of edible oil is taken out from each barrel, the remaining 5/2 1 of barrel A is equal to the remaining 1/3 .. How many kilograms of edible oil are there in each barrel?
Example 6: The number of people in workshop A of a factory is 3/4 of that in workshop B. If 60 people are transferred from workshop B to workshop A, then the number of people in workshop B is 2/3 of that in workshop A. How many people were there in workshop A at that time?
Example 7: The results of primary and secondary schools participating in a city's mathematics competition are as follows: the number of winners in primary and junior high schools accounts for 7/ 1 1, and the number of winners in junior high schools and senior high schools accounts for more than 3/2. There are 43 winners in junior high school. What is the total number of winners?
Example 8: There is a basket of apples. If it is distributed to all students in a class equally, each student can get 6 apples. If only the male students in this class are distributed, everyone can get 10 apples. If it is only distributed to the female students in the class, how much can each person get?
A fruit shop delivered a batch of pears and apples. It is known that 2/620kg of pears and apples, and 1/4 of pears is equal to 2/5 of apples. How many kilograms of pears are there?
There are 60 kilograms of mixed sugar. It consists of four kinds of sugar: milk candy, fruit candy, soft candy and crisp candy, wherein the sum of milk candy and fruit candy accounts for 2/3 of the total weight; The sum of the weight of milk candy and soft candy accounts for 3/4 of the total weight; The sum of the weight of milk sugar and crisp sugar accounts for 60% of the total weight. How many kilograms of each of the four kinds of sugar?
There are two teams in a workshop, and the ratio of the first team to the second team is 5: 3. If there are 14 people in team one to team two, then the ratio of team one to team two is 1:2. How many people are there in each team?
4. Class A and Class B have the same number of students, and some students in each class participate in extracurricular astronomy groups. The number of people in class A who participated in the astronomy group was exactly 1/3 of the number of people in class B who did not participate, and the number of people in class B who participated in the astronomy group was exactly 1/4 of the number of people in class A who did not participate. Ask the number of people who didn't attend class A. What's the number of people who didn't attend class B?
5. The "Nine Chapters Mathematics Bookstore" in Haidian Bookstore offers preferential treatment to customers. Anyone who buys more than 65,438+000 books of a certain kind will get 90% of the book price. A school went to a bookstore and bought two kinds of books, A and B. Among them, the number of books in B was 3/5 of that in A, and only A got a 10% discount. At this time, the total amount paid for purchasing Class A books is twice that paid for purchasing Class B books. Suppose the price of type B book is 1.5 yuan, what is the original price of type A book?