Homework

Kelsey needed some help with her math homework (it was more like a logic problem)...the problem is below and the grid above helped her get her answer...the second problem was kind of fun, but needed no grid (maybe I'm a big dork?)

Problem One:

A shaky story. Stacy and Sam Smyth wer known for throwing a heck of a good party. At one of their wild gatherings, five couples were present (this included the Smyths, of course). The attendees were cordial, some even shook hands with other guests.

Although we have no idea who shook hands with whom, we do know that no one shook hands with themselves or his or her own spouse. Given these facts, a guest might not shake anyone's hand or might shake as many as eight other people's hands. At midnight, Sam Smyth gathered the crowd and asked the nine other guests how many hands each of them had shaken.

Much to Sam's amazement, each person gave a different answer. That is, someone didn't shake any hands, someone else shook one hand, someone else shook two hands, someone else shook three hands and so forth, down to the last person, who shook eight hands. Given this outcome, determine the exact number of hands Stacy Smyth shook.

Problem Two:

Lights out. Two rooms are connected by a hallway that has a bend in it so that it is impossible to see one room while standing in the other. One of the rooms has three light switches. You are told that exactly one of the switches turns on a light in the other room, and the other two are not connected to any lights. What is the fewest number of times you would have to walk to the other room to figure out which switch turns on the light? And the follow up question is: Why is the answer to the preceding question “one”?

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