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
+37157 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.
+37157 Double oops! See tertre 's answer......
23 x 2 / 2 = 23 handshakes !
+4622 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!
+33652 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.
