ZiganZhen
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How to prove handshaking lemma without using graph theory?
The original question was that every person who has ever lived has shaken hands with a certain number of other people. Prove that the number of people who have shaken hands an odd number of times is even. How the prove the statement without graph theory??
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james22
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Since the statement of the lemma uses graph theory, you aren't going to prove it without graph theory unless you have a different statement of it.
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ZiganZhen
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The original question was that every person who has ever lived has shaken hands with a certain number of other people. Prove that the number of people who have shaken hands an odd number of times is even. How to prove it without graph theory???
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ghostwalker
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#4
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(Original post by ZiganZhen)
The original question was that every person who has ever lived has shaken hands with a certain number of other people. Prove that the number of people who have shaken hands an odd number of times is even. How to prove it without graph theory???
Consider the total number of hands shaken. Is it odd or even?

Then consider how hands are shaken each time people shake hands? Odd or even?
Hence....

Graph theory without the graph theory.
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Padwas
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without a graph it will be hard
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ZiganZhen
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(Original post by ghostwalker)
Consider the total number of hands shaken. Is it odd or even?

Then consider how hands are shaken each time people shake hands? Odd or even?
Hence....

Graph theory without the graph theory.
I think I have got it already. Thank you anyway~~~~
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ghostwalker
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(Original post by ZiganZhen)
I think I have got it already. Thank you anyway~~~~
OK.
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IceKidd
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(Original post by ghostwalker)
Consider the total number of hands shaken. Is it odd or even?

Then consider how hands are shaken each time people shake hands? Odd or even?
Hence....

Graph theory without the graph theory.
Yeah its essentially the same ideas as used in graph theory
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ghostwalker
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(Original post by IceKidd)
Yeah its essentially the same ideas as used in graph theory
Hence my comment:

"Graph theory without the graph theory."
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IceKidd
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(Original post by ghostwalker)
Hence my comment:

"Graph theory without the graph theory."
Yeah i wernt trying to put down your argument, sorry if i didnt make that clear.

It was neat
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ghostwalker
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(Original post by IceKidd)
Yeah i wernt trying to put down your argument, sorry if i didnt make that clear.

It was neat
:cool:
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