Tuesday, December 25, 2007

Merry All That

This is what I used to listen to on Christmas Eve as a young lad growing up in what was, practically speaking, Canada. It is quite a listen, and you should check it out.

On the one hand, thinking of this thing that I used to listen to on CBC Radio on Christmas Eves long ago and being able to immediately have it is the greatest thing about modern life. On the other hand, it was nice to happen upon these things by accident, too.


Anonymous said...

I just want to ask a random math question. What is the formula to figure out something like the following?
"A circle has 6 points. How many different quadrilaterals can be made within the circle using the 6 points?" I know that this is way simple because even I can figure it out - but I'm doing it manually (you know - drawing circles with points and connecting the dots)...there must be an actual way to accomplish this.

- lilita's lil' sista

Transient Gadfly said...

It depends on what they mean by "different quadrilaterals." In one case it's pretty math-y, the other it's really not. I give you the long explanation, then the short one.

As with all problems like this, you have to realize something about the problem before you can do the math. In this case, it's this: you've got six points, and four corners, so you have to skip exactly two of the points. So go around the circle, number the points one through six, and figure out all the different ways you can skip two points. You can skip 1 & 2, 1 & 3, 2 & 3, etc. The number there is 6C2 (number of ways you can choose 2 things from six things), which is
6!/((6 - 2)! x 2!) = 15
15 different quadrilaterals, for some definition of "different." Notice, however, that the quadrilateral made by skipping points 1 and 2 is exactly the same as the one made by skipping points 2 and 3, just rotated by 60 degrees. If those two quadrilaterals are the same, then all you needed was the thing about counting the points you skip, and then there's only three different ones: skip 1 & 2, skip 1 & 3, skip 1 & 4. Everything else is a rotation of one of those three.

I assume, especially if this is a question from an LSAT book or the like, that they're looking for the latter answer. However, that's far from clear, and you have my permission to hit the creator of this question with a large blunt object.

Anonymous said...

thank you -
I'm not taking the GRE yet, but considering it. I think i need to take calculus first. You are a great a resource, even for your friend's random little sister.

- lil' sis