Ten people are at a party, and you want everyone to meet (shake hands with) everyone else at the party. How many handshakes will it take?

Question

Solution to this word problem 

Answer 1

Line the ten people in a row.

Have the first person go down the line and shake the hand of the other 9, then leave.

Have the first person go down the line and shake the hand of the other 8, then leave.

Have the first person go down the line and shake the hand of the other 7, then leave.

 

With this pattern, how many handshakes were made?

 

This problem has been often proposed using the Justices of the Supreme Court who shake each other's hand before going to the bench.

 

Answer 2

Hello Bianca,

 

The general solution to this problem is: N*(N-1)/2, thus pertinent to this particular case it would be (10*9)/2= 45 handshakes.

 

A bit of explanation. This math problem can be reduced to another well-known one of calculating the sum of arithmetic progression: thus, for N people that sum would be:

 

1+2+3 +...+(N-1) = N*(N-1)/2

 

For example, the number of handshakes between Justices of the SCOTUS would be: 9*8/2=36, on the US Senate floor it would be 100*99/2 = 4,950 handshakes, and so on.

 

Hope this may help. Best regards,