Good luck to students from Albany Area Math Circle who will be joining middle school students from all over the country--indeed all over the world!--in taking the AMC8 this Tuesday. Back when I was an 8th grader, I never could have imagined that math could be this much fun!
Here's one of my favorite problems from an old AMC8 (#19 2000). (Click on the image to make it larger and clearer.)
There are some tedious and time-consuming ways to solve this problem, but if you think about it for a while, there's a very beautiful and cool "outside the box" way to solve this problem very quickly and elegantly. (Or maybe we should call it a "redefine the box" way to solve the problem!) What is great about the cool "redefine the box" solution is that once you see it, it's very easy to check your work and be sure your answer is correct. (If you do it the tedious, hard way, there are more places to make silly mistakes and go astray.)
For hints and solutions to this and other old AMC8 problems, check out this link.
No matter whether you are taking the AMC8 with Albany Area Math Circle along with students at Hebrew Academy or at your own school (shout-outs and kudos to Iroquois Middle Schools and Van Antwerp Middle Schools, who will be administering the AMC8 for the first time this year!), you will be taking part in a great event along with almost 200,000 strong and enthusiastic problem-solvers around the world!
A few things to remember: