June 1998
We begin with what we know: since nobody shook hands with more than six persons, and the seven people other than
yourself all shook hands with a different number of people, the numbers must have been:
0,1,2,3,4,5,6, respectively.
Let us begin with "0"--whom we shall call the introvert, because this person shook nobody's hand. At the other extreme
was "6"--whom we shall call the extrovert for obvious reasons. The extrovert shook everybody's hand, except his/her
own spouse. Since the extrovert and the introvert did not shake hands, the introvert must be the extrovert's spouse.
0&6 are a couple, leaving 1,2,3,4,5 and yourself
Consider the remaining five people other than yourself. Each of these shook hands with the extrovert, and none with the introvert.
One of these five people-- "1", the quasi-introvert--only shook hands with one other person, the extrovert. Another--
"5", the quasi-extrovert--shook hands with five people, everyone except his/her own spouse and the introvert ("0").
Therefore, the quasi-introvert and the quasi-extrovert form a couple.
0&6, 1&5 are couples, leaving 2,3,4 and yourself.
In the same way, "2" and "4" form a couple--we'll call them the pseudo-introvert and pseudo-extrovert, respectively.
0&6, 1&5, 2&4 are couples, leaving 3 and yourself.
Therefore, your spouse is the one who shook hands with three other persons. Furthermore, you and your spouse shook hands with the same people: the extrovert ("6"), the quasi-extrovert ("5"), and the psuedo-extrovert ("4"). This gregarious group includes Pat (one of our givens: you shook hands with Pat), and therefore must exclude Chris.
Answer: Your spouse shook hands with Pat, but not Chris.
Lloyd Dalton, a senior at St. Cloud State in Minnesota, has put together an outstanding diagram.
Lloyd's Solution
Click for the IBM techexplorer version.
Good luck planning your next party.
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