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

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Discussion Overview

The discussion revolves around a brain teaser involving a party scenario where Mr. and Mrs. Smith and four other couples shake hands. The challenge is to determine how many hands Mrs. Smith shook, given that each participant provided a different number of handshakes.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that Mrs. Smith shook the same number of hands as Mr. Smith, suggesting both shook 4 hands.
  • Others argue against this, noting that since each participant gave a different answer, it implies that all couples shook a different number of hands, thus questioning the assumption that Mr. and Mrs. Smith shook the same number.
  • One participant outlines a reasoning process involving the maximum and minimum number of shakes possible, concluding that Mrs. Smith must have shaken 4 hands based on the distribution of handshakes among the couples.
  • Another participant expresses uncertainty about the solution, highlighting the complexity and potential for multiple interpretations of the handshake counts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the number of hands Mrs. Smith shook. There are competing views regarding the implications of the different handshake counts and the reasoning behind them.

Contextual Notes

The discussion includes assumptions about the distribution of handshakes and the implications of the unique answers given by each participant, which remain unresolved.

Who May Find This Useful

Individuals interested in logic puzzles, mathematical reasoning, and problem-solving challenges may find this discussion engaging.

Galileo
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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?
 
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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. :confused:
 
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
 
i never bithered taking that much trouble

anyways good job.
 
Right on, Randall.
 

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