23 people attend a party. Each person shakes hands with AT LEAST TWO other people. What is the MINIMUM possible number of handshakes?

Can someone please explain the solution?

Also the answer is NOT 12

Guest Sep 18, 2018

edited by
Guest
Sep 18, 2018

#1**+1 **

Each of the 23 people must shake hands with 22 others = 506 BUT TWO people are involved in each handshake, so the real number of handshakes is 506/2 = 253 Handshakes.

ElectricPavlov
Sep 18, 2018

#2**+1 **

Or, we can just plug the value in the handshake formula: n(n-1)/2, 23*22/2=23*11=253 handshakes!

Look at EP's solutions for more information!

tertre
Sep 18, 2018

#6

#8**0 **

Look at it this way:

Label the people from 1 to 9 then continue with letters A to N.

Pair them in the following way:

13 24

35 46

57 68

79 8A

9B AC

BD CE

DF EG

FH GI

HJ IK

JL KM

LN M2

N1

23 pairings with each label occurring exactly twice.

This set of pairings is not unique of course.

Alan
Sep 19, 2018