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        riddles >> easy >> 8 men in a room
        
(Message started by: SgtAcid on Jan 24^th, 2003, 2:51pm)

Title: 8 men in a room
Post by SgtAcid on Jan 24^th, 2003, 2:51pm

8 men are in a room. Each man shakes hands with each of the others once. How many handshakes are there?

Title: Re: 8 men in a room
Post by redPEPPER on Jan 24^th, 2003, 3:05pm

I'd say [hide]28[/hide] but it seems much too easy to be in the medium forum. Maybe there's a catch that I missed?

Title: Re: 8 men in a room
Post by SgtAcid on Jan 24^th, 2003, 3:43pm

maybe you're right it should be in the easy if you got it that easily. This one caused alot of confusion for people at my job, so i thought i'd post it here. Let's see if other people find the answer as easily as you did.

Title: Re: 8 men in a room
Post by udippel on Jan 25^th, 2003, 9:35am

Agreed. For Medium you expect something tricky. Even for Easy it's too ... easy, isn't it? Compared to some quite tricky stuff in there at least.

Title: Re: 8 men in a room
Post by Speaker on Jan 28^th, 2003, 2:03am

OK, my first guess, before peeking, was 56. That is that all eight men must shake hands with seven people. 7 x 8 = 56.

How do you get the hidden answer?

OK, still here, using trusty paper and red, blue and black pens, I sketched it out. And found, 7+6+5+4+3+2+1
I really only needed to draw the red and blue itterations, and then the pattern became clear.

Is there some cool way to do this?

Title: Re: 8 men in a room
Post by towr on Jan 28^th, 2003, 2:22am

yes, take half of 7*8..
in a handshake two people shake hands..
every person shakes everyone else's hand, so everyone shakes the hand of 7 other people, but when A shakes B's hand B also shakes A's hand at the same time, so it's half of 8*7 = 28

Title: Re: 8 men in a room
Post by william wu on Jan 28^th, 2003, 3:23am

Yeah it's easy. Sorry SgtAcid :) Cool post towr.

Here's perhaps an even easier way to think about it. There are eight people. If you choose any 2 of those people, they must have shook hands. Thus there must have been 8 choose 2 handshakes. C(8,2) = 8*7 / 2 = 28.

Another way: computer scientists should quickly recognize that this question asks for the number of edges in a clique with 8 vertices. A clique with n vertices has C(n,2) = n(n-1)/2 edges.

Note: In case anyone is unacquainted: The C(n,k) operation is referred to as "n choose k" and simply returns the number of ways to choose k things out of n things. The formula is C(n,k) = n! / (k! (n-k)!.

Title: Re: 8 men in a room
Post by redPEPPER on Jan 28^th, 2003, 7:31am

on 01/28/03 at 03:23:44, william wu wrote:

Note: In case anyone is unacquainted: The C(n,k) operation is referred to as "n choose k" and simply returns the number of ways to choose k things out of n things.

English is not my native language, but I seem to have found another way to call C(n,k) that's almost a perfect translation of the French version: C(n,k) is a combination of k elements among n. Is that another proper way to say it? Is "n choose k" more popular, or just shorter? Just trying to improve my vocabulary here.

Quote:

The formula is C(n,k) = n! / (k! (n-k)!.

That is, if you don't forget to close all your brackets ;)

C(n,k) = n! / (k! (n-k)!)

Title: Re: 8 men in a room
Post by william wu on Jan 28^th, 2003, 11:26am

I think n choose k is both shorter and more popular, at least here in the States. Popular because it's short.

Title: Re: 8 men in a room
Post by Iceburg9988 on Jun 7^th, 2003, 3:45pm

The way to figure out the solution: use theortical probability. We learned this is school.
1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8
1,2 2,3 3,4 4,5 5,6 6,7 7,8
1,3 2,4 3,5 4,6 5,7 6,8
1,4 2,5 3,6 4,7 5,8
1,5 2,6 3,7 4,8
1,6 2,7 3,8
1,7 2,8
1,8
Meaning there are 36 handshakes! (I think, thank my math teacher for that ^-^)

Title: Re: 8 men in a room
Post by Iceburg9988 on Jun 7^th, 2003, 3:46pm

Hehe, I'm only 10 years old! ^-^

Title: Re: 8 men in a room
Post by THUDandBLUNDER on Jun 7^th, 2003, 4:28pm

Hi Iceburg9988 (aged 10)!

Quote:

1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8

Do the men shake hands with themselves? ???

Title: Re: 8 men in a room
Post by Icey9988 on Jul 25^th, 2004, 6:37pm

holy crap youre right and this is 2 years after! im 12 years old for friggin sakes and its still here?!? O.O;; sorry aobut that post - i was using a way to find out the probability of 2 dice. you're right. sry peoples hehe.