Weekly solution 9 – solution
Handshakes
Your spouse shook hands with Pat, but not Chris.
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 pseudo-extrovert (“4″). This gregarious group includes Pat (one of our givens: you shook hands with Pat), and therefore must exclude Chris.
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What is it most interesting about this puzzle is that, the answer it’s still the same even if the party had a thousand couples: Pat, yes, Chris, no, third question, well it would have be tough to explain as you did. Sorry for the obfuscation in my previous comment… did you noted at least that Mars appeared 3 times in the text?
As I said that time, I was near to present the right result through the wrong reasoning. I guessed that, if I shook hands only with Pat, then he should have been the one to shook hands with everyone… because I surely shook hands with that guy. And his spouse Chris, surely must have be the one to not shook hands with anyone, being the only one not entitled to do that with her spouse (not sure who are female or male’s names here, sorry). This solved the problem except that, when I tried to see what happened with other couples, I discovered the case to be impossible. The text lead me to think I shook hands with only one, but that scenario is a dead end. On close attention, the fact that it is referred I shook Pat’s hands does not mean I only shook those. So back to the square one, and to find what in the end, was the reasoning you presented here.