Everything that doesn't matter has no mass.

Dang it, I can't find a way to incorporate LaTeX into Blogger! LaTeX is this spiffy little program that can churn out really nice typesetting in mathematics. Of course I could always blog over at the math forum, but there's not much freedom in creating a template for your blog, so everyone's blog looks the same (zzzz!). I could copy-paste pictures of LaTeX-created equations but that's just too much bother and looks real ugly, as I believe you can see from one of my posts from a year ago.

But perhaps it's really all for the best that I can't use LaTeX, or I would bore all of you with some really neat little math problems that I solved today. :P

Actually, here's one that involves no equations at all:

One morning each member of Angela's family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?

My solution:

1/4 M + 1/6 C = 8 ---- (1)

We know M + C must be divisible by 8

Multiplying (1) by 4, we have

M + 4/6 C = 32

Multiplying (1) by 6, we have

3/2 M + C = 48

But, (M + 4/6 C) < (M + C) < (3/2 M + C), i.e. 32 < ( M + C) <>Therefore, M + C = 40, and there are 5 members in the family.

OK, it's not all that difficult, but I just like how far-out this problem is - I never would have dreamed up a problem like this in a million years. Problem source: USA AMC10 2000. Haha, I know I'm a little too old for this competition, but in my defense it is also one of the problems in the USA AMC12 2000, which I'm still young enough to compete in. Well, the truth is I've been out of touch with problem solving for too long, and need to start somewhere so I ended up doing the AMC10 paper. I'm proud to say - no snags encountered at all in that paper!

By now it must be obvious that I have too much free time. I've decided that I need to improve my knowledge of the geography of the US, so tomorrow I will memorise all 50 states and their state capitals. A little head start here: Surprisingly, the capital of the state of New York is not New York City, but Albany!