Two thinking questions

1. How many children are there in kindergarten?
The teacher arranged the children in the kindergarten in a row and started sending fruit. The teacher distributes fruit in the following way:
Start with the first person on the left, and send a pear at every two people; start with the first person on the right, and send an apple at every four people. If
After the distribution, 10 children both get pears and apples. How many children are there in this kindergarten?

Analysis:

Assume this line is A1 .... ap... al .... AQ .., AP, Al, AQ are people who have both pears and apples, and they have no more pears and apples, so what is the distance between any two who have both pears and apples?

The distance between the apple kids is 3, and the distance between the girls who get the pears is 5. To make them take both the pears and the apples, the distance must be their least common factor, D = lcm (3, 5) = 15

In this way, the distance between the person with both pears and apples on the leftmost side and the person with both pears and apples on the rightmost side can be calculated. D * (10-1) + 1.

This is the minimum number of people.

Number of people value formula:

N = D × (10-1) + 1 + 3A + 5b

A can be 0, 1, 2, 4 B, 0, 1, 2

A total of 15 values.

Maximum = 136 + 4*3 + 10 = 158

Take 0a, 1a, 2a, 3A, 4A on the left, and take a multiple of A to ensure that the AP can get an apple, not greater than 4A is to ensure that the AP is the person with both pears and apples at the leftmost end.

The analysis is the same on the right side.

 

2. There are 25 horses running five horses each round. Apart from the sequence of horses in the wheel, the time of the horse running cannot be recorded. You can ask how many rounds of horse running are required to run the top three.

Analysis:

1. It takes 5 rounds to run all horses.

2. In the sixth round, the first place in each round is the sixth round. After the sixth round, the first place can be determined.

3. however, two or three names are to be determined, because it is possible that the first team is the second in the round, and the third is better than the current two or three, at the same time, the second place in the round of 2nd teams may be faster than the current 3rd.

4. According to the above analysis, the number of horses running in the 7th round was 2 or 3 in the 1st round, the second in the 2nd round, and the current number was 2nd and 3rd.

5. The answer is 7.