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# Five people meet and exchange handshakes. If exactly 3 of

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CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 705 [0], given: 781

Five people meet and exchange handshakes. If exactly 3 of [#permalink]  13 Sep 2003, 03:32
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Five people meet and exchange handshakes. If exactly 3 of the
people each shake hands with 3 people, and if 1 people shakes hands
with 1 other person. Then what is the least number of handshakes that
could have been exchanged?
Senior Manager
Joined: 22 May 2003
Posts: 334
Location: Uruguay
Followers: 1

Kudos [?]: 38 [0], given: 0

I get 6

If we have 5 people: A,B,D,E and F

A,B,D must shake 3 times each
F must shake once at least

If ABD shake hands with one another we have 3 different shakes so far.

And A,B and D still have to make another shake.

A shakes E (we have 4 shakes now)
B shakes E (we have 5 shakes)
C shakes F (we have 6 shakes)
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 705 [0], given: 781

Re: PS : Handshakes [#permalink]  07 Oct 2003, 05:12
praetorian123 wrote:
Five people meet and exchange handshakes. If exactly 3 of the
people each shake hands with 3 people, and if 1 people shakes hands
with 1 other person. Then what is the least number of handshakes that
could have been exchanged?

3 people shake hands ... 3*2/2 = 3

1 person shakes hand with another = 1

Remaining one shakes hands with another one = 1

i would say 5

dont have the official answer...stolyar ...help!!

Thanks
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 78 [0], given: 0

I got 7.

A B C D E

A, B, and C handshake one another = 3 (each shakes the other two)
A, B, and C handshake D=3 (in total A, B and C make 3 shakes each)
E handshakes D one time

Thus, I have 7.
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 705 [0], given: 781

stolyar wrote:
I got 7.

A B C D E

A, B, and C handshake one another = 3 (each shakes the other two)
A, B, and C handshake D=3 (in total A, B and C make 3 shakes each)
E handshakes D one time

Thus, I have 7.

simple problem, but oh well! I think thats correct.

thanks
praetorian
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