Math Contest Done

Today's weather: High = 14 Low = 8
Cloudy

Last week, students at our school wrote the annual Fermat and Cayley math contests designed by the University of Waterloo. Interestingly enough, that same university is coming to our school next week to do a math workshop, and they are offering masters degrees for teachers. Definitely count me in on that!!

The math contest is of course very tough. It's optional for students to write back home in BC, but here, the principal requires that the students write. Good for him. Since the Chinese students at our school boast about how good they are in math (and it is certainly true, they are exceptional), then it only makes sense they are all required to write a contest.

Compared to previous years' contests, I didn't find this one very difficult, in fact it was slightly easier. Of course, it's still a contest, but when I constructed an answer key to go over the questions for next class, none of my solutions took any longer than a few lines. In some of the previous contests, the solutions could take 2 pages or more.

The Fermat Contest for Gr 11 is completely multiple choice, and consists of 25 questions. Students really struggled on this one, however, and the trend was to leave many of the last 5 questions blank. If they do that, they still get 2 marks for each blank -- whereas they get zero for guessing a wrong answer. The safer option is to leave it blank and then forfeit the difference of marks for that question. Students who are both intelligent and brave will take the risk and make an educated guess on some of the last 5 questions, and hopefully beat out those who take the safer path.

Of course, the smartest students would actually do those difficult questions, but the biggest problem is time. With only 60 minutes to work with, there just isn't TIME for any formal proofs or constructing elaborate solutions like that which appear in the keys. Nobody I know has actually finished the test with time to spare. The ability to make educated multiple choice guesses is what separates the men from the boys on this contest.

For example, the second-last question appears as follows:

"Four numbers w, x, y, z satisfy w < x < y < z. Each of the six possible pairs of distinct numbers has a different sum. The four smallest sums are 1, 2, 3, and 4. What is the sum of all possible values of z?"

The linchpin in this problem is about how to rank the 6 sums from smallest to largest.
It is pretty easy to show that (w + x) < (w + y) for the 2 smallest sums
It is also easy to show that (x + z) < (y + z) for the 2 largest sums
The part where we run into trouble is the two middle sums
In other words, how to show if (w + z) < (x + y) or the other way around.

At this point, rather than wasting precious contest time struggling with this ambiguity, why not just assume that either one of the cases is true, and then look at each case seperately. Once that part is figured out, the rest of the question is just mechanics.

Case 1: x + z = 3 so then y + z = 4 and then make two other equations from the 2 smallest sums
Case 2: x + z = 4 so then y + z = 3 and then make two other equations from the 2 smallest sums


Anyways, I'm eager to find out the results from this contest.

Back in the City

Today's weather: High = 8 Low = 2
Showers

After a rather relaxing and adventurous bicycle trip which you can read about on my travel blog, it is now back to work in Shanghai

http://www.travelblog.org/Asia/China/Shanghai/Xujiahui/blog-572209.html

It's nice to be back as both the city and the work are good. The weather is going to see major improvements in the coming weeks as we finally get out of this winter slump and back to reasonable 15-20 degree highs. Of course, I really got spoiled while enjoying tropical temperatures in Thailand and Indonesia. On the other hand, the body adjusts so quickly to different climates that it's almost as if the trip never happened. Thankfully, the pictures prove that it did.