# Brain Teaser: How Many Hands Did Mrs. Smith Shake?

• Galileo
In summary, Mr. and Mrs. Smith invited four other couples to their party. When everyone arrived, they shook hands with each other, except for their spouses and themselves. Afterwards, Mr. Smith asked everyone how many hands they shook and received a different answer from each of them. The question was how many hands Mrs. Smith shook, and the answer is 4, based on the fact that she and Mr. Smith were part of one of the five couples and he received 9 different answers from the others.
Galileo
Homework Helper
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?

Galileo said:
The question is: How many hands did Mrs. Smith shake?
IN WHITE
The same as Mr Smith 4
Someone else will explain.

Last edited:
RandallB said:
The same as Mr Smith 4
Someone else will explain.

well, i am not really sure about the 4, but i don't 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 don't see how you concluded that mr. and mrs. smith shook same no. of hands.

also, i don't 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.

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

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.

he must be part of couple 5.
Therefore Mrs Smith had 4 shakes.

Work for you?
Good one Galileo!
RB

i never bithered taking that much trouble

anyways good job.

Right on, Randall.

## 1. How can we determine the number of hands Mrs. Smith shook?

The number of hands Mrs. Smith shook can be determined by counting the number of people she shook hands with and multiplying it by two, as each person has two hands.

## 2. Is there any additional information that would help us solve this brain teaser?

Yes, knowing the total number of people in the group or the total number of handshakes in the group would provide crucial information for solving this brain teaser.

## 3. Can we assume that Mrs. Smith only shook hands with people in the group?

No, we cannot make this assumption. Mrs. Smith could have also shaken hands with people outside the group, which would affect the total number of hands she shook.

## 4. What is the significance of this brain teaser?

This brain teaser is meant to test our ability to think critically and logically. It also highlights the importance of paying attention to details and considering all possible scenarios before jumping to a conclusion.

## 5. Is there a mathematical formula that can be used to solve this brain teaser?

Yes, this brain teaser can be solved using the formula n(n-1)/2, where n represents the number of people in the group. This formula gives the total number of handshakes in a group of n people.

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