Even - Odd Handshake ProblemDate: 05/11/2000 at 18:06:15 From: Josh Cox Subject: Handshake problem Dr. Math, Every person on the earth has shaken a certain number of hands. Prove that the number of persons who have shaken an odd number of hands is even. I understand that this problem is true from experimental research I conducted on paper. However, I am unsure how to prove this problem works for every situation. Could you please help me to prove it? I would really appreciate it. Thanks! Date: 05/11/2000 at 18:46:21 From: Doctor Wilkinson Subject: Re: Handshake problem Very cute problem, Josh! If you add up the number of hands each person has shaken, you have to end up with an even number, because every handshake gets counted twice. Now the sum of any number of even numbers is even, and the sum of an odd number of odd numbers is odd, and the sum of an even number and an odd number is odd; so the number of persons who have shaken an odd number of hands must be even, not odd. - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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