Cool Math Problem

[susy_gwen]

So, I gave my geometry question yesterday, but didn't find the solution until this morning. And it's not what I was expecting. Because it's so interesting, I'd thought I'd challenge all of you with it. I'll post the answer tonight. So, have fun and enjoy!

Who Shook Who’s Hand?The Bakers had a barbeque in their back yard. They invited three

Comments

[sannalim]

I saw angua9's answer (sans diagram) already, but haven't looked at any of the other comments that came in while I was working on my answer. I'm afraid I must beg to differ with our esteemed Queen ORX and say that the answer is THREE.

* No-one shook hands with Mr B because he was at the grill finishing the hamburgers. For all intents and purposes, we can pretend he doesn't exist.

* Each of the six visitors shook hands a different number of times, but nothing in the wording of the question prevents Mrs B from having shaken hands the same number of times as one of her guests.

* Mrs B plus six guests makes seven. It's silly to think of shaking your own hand, so the maximum number of handshakes one person could have made is N - 1 = 6. Theoretically one of the guests could have been very antisocial that evening and given zero handshakes, in which case the maximum possible number of handshakes is five.

Continuing with a maximum of six (I'll treat the case of max = 5 a bit later)

* The person who gave only one handshake must have shaken hands with the person who shook hands six times

* The person who gave only two handshakes must have shaken hands with the person who shook hands five times

At this point, we can draw this graph, where each node is a person and each line a handshake.

The person who shook hands with four people can be put in three different ways: like this, like this, or like this.

There are always two people who shook hands three times; one of those people is Mrs B and the other is one of the guests.

* If we assume that one of the guests had a cold and didn't want to shake hands, the max becomes five and the min becomes zero. In this case the final diagram--there is only one--looks like this.

There are still two people who shook hands three times; one of those people is Mrs B and the other is one of the guests.