The Logical Puzzle - 26 Oct 2006

October’s Puzzle: Shaking Hands
My wife and I were at a party recently with four other married couples. All the people who didn't know each other shook hands. Of course, each person knew his or her spouse. I asked each of the nine other people at the party how many hands they shook and received all possible answers ranging from 0 through 8. Each person shook a different number of hands. What was my wife's answer?

Let’s start with the person who shook eight hands. All others (including myself and excluding that person’s spouse) shook at least that person's hand, so everyone else shook at least one hand. Therefore, that person’s spouse must be the person who shook zero hands. That's the tricky part. Now, take the couple who shook eight and zero hands out of the equation. To do so, subtract one from the answers of all remaining individuals. Simply imagine that you’re now facing the same puzzle, but with four couples, and with the seven individuals besides me replying to my question with the answers 0 through 6.

You'll quickly conclue that the five couples, including me and my wife, shook hands in the following manner: 8/0, 7/1, 6/2, 5/3, 4/4. Because I asked nine individuals how many hands they shook, and I got nine unique answers, my wife and I must be the couple who shook four hands each. Hence, my wife shook four hands.

November's Puzzle: Then There Were Five?
I got this puzzle from my good friend Dejan Sarka. It involves a mix of logic and English. Can you think of a sentence that contains the word "and" five times consecutively ("and and and and and")? The sentence must make sense. In other words, I'm not aiming for a sentence such as "Five times 'and' are and and and and and." Rather, the sentence should make sense without such silly tricks.