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Started by bonanova, Dec 22 2007 01:35 PM

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#1 bonanova

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Posted 22 December 2007 - 01:35 PM

You and your spouse invite four other couples to a party. Ten people in all.
Prior to the party each person [other than you] knew a different number of people present.

How many people did your spouse know?
How many did you know?

You may assume the following:
If A knows B, then B knows A.
Every male knows his partner.
You might have invited people you don't know.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 PDR

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Posted 22 December 2007 - 05:39 PM

if a knows b then b knows a
every male knows his partner
therefore every partner knows her male :o

everyone knows at least 1 person (their partner)
there are 9 people who must know at least 1 person
the most anyone can know is 9
no two can know the same number of people - other than one person who can (and must) know the same number of people as you
therefore one person knows only 1 other, one knows 2, etc through the last person who knows 9 other people
the partner of the person who knows 9 can only know one person (their partner)
follow the logic, so the answer must be...
Spoiler for solution

PS - great puzzle - keep 'em coming... :)
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