prove that the # of people through all of history who have shaken hands an odd number of times is even?

Question

lets see a formal proof folks!!

they shake hands normally. i.e., not with more than 2 or more others at once, and not with themselves.

Answer 1

o = Number of people shaken hands an odd number of times
e = Number of people shaken hands an even number of times (including people that have shaken 0 hands).

o and e start at 0.

Every time a hand shake occurs the following events can happen.
Two o people shake hands and both become e
o decrements by 2
e increments by 2
Two e people shake hands and both become o
o increments by 2
e decrements by 2
And o shakes hands with an e. And switch places.
o and e stay the same.

Since o starts with 0 and all combinations of hand shakes can only increment or decrement o by 2, o must always be even.

Answer 2

Even though it takes two people to shake hands people don't always shake hands with just one other person, so one person can shake hands an odd number of times and the people he shook hands with could shake hands an even number of times. The question is not provable...

Answer 3

well if you count the fact that 2 people shake hands it can only be even

Answer 4

because it take 2 people to shake hands....so n e number multiplied by 2 is an even number...i just got that...nice one...

Answer 5

it take two hands to shake..and 2 or its multiples cannot be odd

Answer 6

But surely, it would be ODD if the number of times were EVEN.
EVEN if it was ODD, surely it could be EVEN>>>>

Answer 7

dumb question. TOO MUCH DRUGGSS

Answer 8

what?