# Handshakes brain teaser

1. Feb 16, 2005

### Galileo

Mr. Smith and his wife Mrs. Smith invited four other couples to a party.
When everyone arrived, some shook hands with some of the others. Ofcourse, no one shook hands with his/her spouse or him/herself and none shook hands with the same person twice.

Afterwards Mr. Smith asked everyone how many hands they shook and he received a different answer from each of them.

The question is: How many hands did Mrs. Smith shake?

2. Feb 16, 2005

### RandallB

IN WHITE
The same as Mr Smith 4
Someone else will explain.

Last edited: Feb 16, 2005
3. Feb 25, 2005

### vikasj007

well, i am not really sure about the 4, but i dont think that they will be same as Mr. smith. galileo said that each one of them gave a different answer, it means that all the couples shook different no. of hands. thus i dont see how you concluded that mr. and mrs. smith shook same no. of hands.

also, i dont see how can this possibly be solved, as there is a huge uncertianity about how many hands each shook. maybe, its better if you explain that yourself.

4. Feb 25, 2005

### RandallB

Sure

Total Ten people.
Max # of Shakes for one = 8 (All in the other 4 couples)
Min # of Shakes = 0
Total options of shakes = 9 (0 thru 8)
. . . Oh OH (looks like trouble with10 people!)

Star with First couple that included
Person with 8 shakes - with all
Since all others have at least 1 then
this spouse must have 0 shakes

Next; 2nd couple where one has 7 shakes
except for the one with zero all now have at least 2
thus this spouse must have 1 shake

3rd couple where one has max of 6 shakes
ie not with persons with 0, or 1, and this spouse
already has 2 shakes

4th couple has one w/ max of 5 shakes
ie not with pesons with 0, or 1, and this spouse
will stay at 3 shakes

5th couple - Man has 4 shakes
and wife has 4 shakes
from the 4 above with 5 or more.

Since MR smith got 9 different answers, by not asking himself,
he must be part of couple 5.
Therefore Mrs Smith had 4 shakes.

Work for you?
Good one Galileo!
RB

5. Feb 26, 2005

### vikasj007

i never bithered taking that much trouble

anyways good job.

6. Feb 27, 2005

### Galileo

Right on, Randall.