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Handshakes brain teaser

  1. Feb 16, 2005 #1


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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?
  2. jcsd
  3. Feb 16, 2005 #2
    The same as Mr Smith 4
    Someone else will explain.
    Last edited: Feb 16, 2005
  4. Feb 25, 2005 #3
    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. :confused:
  5. Feb 25, 2005 #4

    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!
  6. Feb 26, 2005 #5
    i never bithered taking that much trouble

    anyways good job.
  7. Feb 27, 2005 #6


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    Right on, Randall.
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