There are n couples participating in a meeting. Each of them belongs to a chat group for a period of time, which is called group. Each of them and his or her spouse are never in the same group. In addition, every two of them are in the same group once, which proves that if n ≥ 4, then the total number of groups K ≥ 2n Why is there a total number of groups ＞ = 2 + (n-1) (n-2) when a member participates in two groups? Is n = 3 also true in this case? Why is the total number of a member participating in three or more groups > = 2n?

There are n couples participating in a meeting. Each of them belongs to a chat group for a period of time, which is called group. Each of them and his or her spouse are never in the same group. In addition, every two of them are in the same group once, which proves that if n ≥ 4, then the total number of groups K ≥ 2n Why is there a total number of groups ＞ = 2 + (n-1) (n-2) when a member participates in two groups? Is n = 3 also true in this case? Why is the total number of a member participating in three or more groups > = 2n?

Well, it's very difficult

There are six couples attending a party. Each man shakes hands with each other (excluding his wife), and the women do not shake hands with each other. How many times do these 12 people shake hands?

Six men shake hands in pairs, each man and the other five men shake hands once, a total of 5 × 6 = 30 (Times), but these 30 handshakes have repeated calculation, so six men shake hands with each other, a total of 30 △ 2 = 15 (Times); men shake hands with women, a total of 6 × 5 = 30 (Times), so these 12 people shake hands: 15 + 30 = 45 (Times). A: these 12 people shake hands 45 times

A and B leave from a and B at the same time and meet each other in two hours. After meeting, the two vehicles continue to move forward. When a arrives at B, B is 60 kilometers away from A. the speed ratio of the two vehicles is known to be 3:2?

If the whole process is regarded as unit "1", then the distance between a and B is 60 (1-12 × 43) = 60 / 13, = 180 (km). The speed sum of a and B is 180 / 2 = 90 (km)

The distance between a and B is 240 km. AB two cars leave from two places at the same time. Two minutes and three hours later, they meet
The distance between a and B is 240 kilometers. AB and ab leave each other at the same time. They meet three minutes later. It is known that the speed ratio of AB and ab is 3:2. What is the speed of each car?

240 △ 3 / 2 = 160 (km / h) this result is the sum of the speeds of AB and ab vehicles
The speed of a is 160 △ (3 + 2) × 3 = 96 (km / h)
B's speed is 160-96 = 64 km / h
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