This Week's Puzzler: Whole Lotta Hand-Shakin' Going On  (1/25/2005)

RAY: John and Mary are married. They agree to go out to dinner with four other 
married couples. So, there are five couples, or ten people, altogether.

They arrive at the restaurant, and, because there are some people who don't know
 other people, there are some handshakes that take place, and introductions. 
Anyone who doesn't know somebody will shake hands with that person. People will 
not shake hands with anyone they already know, and, of course, you don't shake 
hands with your own spouse.

TOM: Unless you're meeting her for the first time.

RAY: Right. At the end of the dinner, John asks all the people there, including 
his own wife, how many hands each of them shook.

He gets the following answers: 0,1,2,3,4,5,6,7, and 8.

There are 9 other people there, and they give him 9 different answers. 

Here's the question: How many hands did John's wife Mary shake?

Now it may seem that you don't have anywhere near enough information to solve 
this problem. But you do.



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Puzzle No. 095
A, B, C, D, E, F, and G are having an argument about which day of the week it is. They speak as follows: 

A: The day after tomorrow is Wednesday. 
B: No, it is Wednesday today. 
C: You are both wrong; it is wednesday tomorrow. 
D: Nonsense. Today is neither Monday, Tuesday, nor Wednesday. 
E: I'm quite sure yesterday was Thursday. 
F: No, tomorrow is Thursday. 
G: All I know is that yesterday was not Saturday. 
If only one of the remarks is true, what day of the week is it? 

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Solution to Puzzle No. 095
We rewrite the statements in the following form: 

Today is Monday. 
Today is Wednesday. 
Today is Tuesday. 
Today is either Thursday, Friday, Saturday or Sunday. 
Today is Friday. 
Today is Wednesday. 
Today is either Saturday, Monday, Tuesday, Wednesday, Thursday or Friday. 
The only day that is not mentioned twice is Sunday, so today is Sunday!