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# Probability Problem

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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

Sep 18, 2018
edited by Guest  Sep 18, 2018

#1
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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.

Sep 18, 2018
#3
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No! Each must shake hands with 2 others.

Guest Sep 18, 2018
#5
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Double oops!    See tertre 's answer......

23 x 2  / 2 = 23 handshakes !

ElectricPavlov  Sep 18, 2018
edited by ElectricPavlov  Sep 18, 2018
#2
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Or, we can just plug the value in the handshake formula: n(n-1)/2, 23*22/2=23*11=253 handshakes!

Sep 18, 2018
#4
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Oops, then it's 23 handshakes!

Sep 18, 2018
#6
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Can you explain how you got 23? Thanks in advance!

Sep 18, 2018
edited by Guest  Sep 18, 2018
#8
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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
#9
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Okay, thanks!

Guest Sep 19, 2018
#7
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23  times 2 = 46

Isn't it 46???????

Sep 19, 2018
#10
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Nice, Alan.....

Sep 19, 2018
edited by CPhill  Sep 20, 2018