# The insane speed of the Mathcounts final

[note: published w/o much of any editing because we were heading out for a Memorial day hike]

Last week Kate Nowak tweeted about one of Art of Problem Solving’s contest prep programs:

This program from AoPS is timed, another one called Alcumus is not.

My kids practice with some of the AMC 8 and 10 exams and have also participated in the MOEMS competitions, too, but we haven’t really done anything with the compeitions requiring insane speed yet. I’m not sure if that type of competition is going to interest them, but if it does then I’m sure Art of Problem Solving’s training is going to be something that we use.

We had some people over for dinner last night and the conversation turned to some of these speed compeititons because one of the kids had just been part of a science bowl team. I don’t actually know anything about the science bowl stuff, but since she mentioned the speed I thought it would be fun to show everyone a video from an old Mathcounts national final because the speed is just unbelievable. One of the competitors here – Bobby Shen – went on to be a 2 time gold medalist at the IMO and also was one of the winners in the Putnam exam last year. Just watch the first couple of questions to see what I mean about the speed:

For our Family math project today I though it would be fun to go through some of these questions with the boys. I had two goals. The first was simply to think through the problems, and fortunately the boys found all of the problems to be pretty engaging. The second was to try to understand how anyone could solve these problems so quickly.

So, following the problem sequence in the video above, here’s the first problem:

The graph of 16x – 2y = 48 intersects the y-axis at (a,b). What is a + b. Mathcounts solution time – 2 seconds, maybe.

Question 2: A rhombus had sides 10 inches. The lengths of the diagonals differ by 4 inches. What is the area of the rhombus? Mathcounts answer time – 1 second or so.

Question 3: When dribbling a basketball up the court Gloria dribbles at a rate of two dribbles for every 3 steps she takes. How many dribbles does she take in her 51 steps up the court? Mathcounts answer time – about 1 second.

Question 4: This a geometry problem, so probably easier to listen to it. This one actually gave the competitors a bit of trouble, too, so it is interesting to see.

Question 5: When you multiply $(x^7 - 2x^4 + 5x^3 + x - 9) * (-3x^6 - 3x^4 + 4x^3 - 5x^2 + 1)$ what is the coefficient of $x^4$? Mathcounts answer time: about 2 seconds.

Question 6: The average age of 3 members of a quartet is 57 years. The average age of the whole quartet is 62. What is the age of the 4th member? Mathcounts answer time – about 2 seconds.

Question 7: This was the first question for the final 2 competitors.

What is the area in square units of a parallelogram having diagonals 8 and 5 that make a 45 degree angle with each other.

This question was pretty hard for my kids, but we got there in about 10 minutes which was nice.

So, a fun morning with some problems from an old Mathcounts exam. Amazing to see the speed of the fastest kids in the country, but also really fun to work through these problems with the boys.