Three married couples arrange a party. They arrive at the party one at a time, the couples not necessarily arriving together. They all, upon arriving, shake the hand of everyone already there, except their own spouse. When everyone has arrived, someone asks all the others how many hands they shook upon arriving, and gets five different answers. How many hands did he himself shake upon arriving?

- anonymous

- chestercat

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- experimentX

?? five different answers ??

- anonymous

5 ?

- anonymous

five..

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## More answers

- anonymous

The answer is he shook 2 people's hands.

- anonymous

how?

- anonymous

@FoolFor, how could u get the answer?

- experimentX

must be six .. because there are 3 couples .. and this seventh person is an outsider

- anonymous

This is a very old combinatoric puzzle.

- experimentX

but i there were 3 couples and they shook each other hand .. except of their own spouse ... they they must have shaken hand 4 times ... each of them ...but why 5 different answers would come??

- experimentX

@JoshDavoll if the person was insider .. then answer must be 4

- apoorvk

he asked 5 people means including him, there were 6. that means he was the last to arrive.
so, he shook 4. he didnt shake his own hands definitely, and definitely not with his spouse.

- anonymous

the answer is 2

- apoorvk

yeah, if he was the insider as you say.

- anonymous

i have a solution, gimme a sec

- inkyvoyd

@FoolForMath is probably correct.

- anonymous

http://www.gottfriedville.net/mathprob/misc-shakes2.html

- anonymous

he asked them after all this happened, i think you misunderstand

- anonymous

number the couples 1 , 2 , 3

- anonymous

so m1 is male from couple 1 , and f1 is female from couple 1

- anonymous

etc etc

- experimentX

if he asked without shaking hand .. and the pair couple shook hand 3 times while the unpaired couple shook 4 times

- anonymous

first to arrive is m1, he shakes 0 peoples hands
second is m2 he shakes 1
third is m3 he shakes 2
fourth is f1 she also shakes 2
fifth is f2 she shakes 3
sixth is f3 she shakes 4
the asker is either m3 or f1 , and they get 5 different answers

- anonymous

Ah i get it now, thanks for explaining it :)

- experimentX

how many hands ON ARRIVING?? i think i understood the question now.

- anonymous

of course we haven't checked thats the only solution, but you can change around the numbers to get a solution that looks different but is the same

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