Monday, June 11, 2007

Mystery Question 6-11-07

This week's question should be fairly simple for some. For people like me, not so much:
I was going through some old family photos in the attic when I stumbled upon our family tree. I studied it for a couple minutes then went back down stairs to tell my mom about the family tree. The problem is I didn't study it long enough to remember the whole thing. I only remembered a couple things about it, and recent memories. Can you help me figure out my family tree? There are two grandparents, who had two children, who both got married and had 2 more children each. Totaling 10 people in all (Alex, David, Jamie, Jessica, John, Justin, Lincoln, Martha, Mary and Tina).

1. One of Jamie's ancestors was David.

2. John's sister gave birth to Tina.

3. Mary went bowling with her nephew last Saturday.

4. Alex is cousins with one of the girls.

5. Justin married Mary.

6. Jessica is not an ancestor, nor cousin of Tina.

7. Lincoln's brother showed Justin's son his baseball cards.
Here is the answer to last week's puzzle. Glad to see it encouraged some great answers!

The first guy to guess (guy #10) will be the only one to assume the following value for the words "white" and "black": The answer "black" will mean that there are an odd number of black hats that he sees. The answer "white" will mean that there are an odd number of white hats that he sees. This way one by one all the other 9 people will know the color of their hats.
Let us say that guy #10 (first to speak, and sees the hats of the remaining 9) says "white". That should mean to everybody else that he sees an odd number of white hats. At this time guy #9 will either be wearing a white or a black hat. If he is wearing a white hat he will only see an even number of white hats, and since guy #10 said that there is and odd number of white hats, guy #9 will know that he is wearing white and will say it. But if guy #9 is wearing a black hat, he will see an odd number of white hats (just like #10 did), and thus will know that he is wearing a black hat and will say it. No matter what #9 answers, guy #8 (who heard guy #10 and guy #9) can now easily incorporate the color of hat on guy #9 into the original answer of guy #10. This will allow #8 to know if he should see an odd or even number of white hats in front of him to determine his own hat color. The same thing repeats with #7-1. And they all get it right except of course #10, though he may get lucky.