There were 20 at a round table at dinner, each of whom shook hands with the person on his or her immediate right and left.At the end of dinner, each person got up and shook hands with everybody except the people who sat to his or her immediate right or left at dinner.Find the number of handshakes that took place after dinner.

Every person shakes hands with 19 people, so at first sight there are 20×19=380 handshakes. But by every handshake two people are involved. So 380 is the result of double-counting. There are 190 handshakes.

Thank you!

To find the number of handshakes that took place after dinner, we need to determine how many handshakes each person made.

Let's start by calculating the number of handshakes each person made during dinner. Since each person shook hands with the person on their immediate right and left, each person made 2 handshakes during dinner.

To find the number of handshakes each person made after dinner, we need to subtract the 2 handshakes they made during dinner from the total number of people at the table, which is 20.

So, each person made 20 - 2 = 18 handshakes after dinner.

Since there were 20 people at the table, we can multiply the number of handshakes each person made after dinner (18) by the number of people (20) to get the total number of handshakes after dinner.

Total number of handshakes after dinner = 18 x 20 = 360 handshakes.

Therefore, there were 360 handshakes that took place after dinner.