Problem of the Week

The Problem of the Week is a set of problems that surround an event, holiday, math concept, etc. A new set is posted on Monday of each week and the solutions are available on the Monday of the following week in the Problem of the Week Archive.

Problem of the Week - National Countdown Round

Click here to download the problem.

During the 2013 Raytheon MATHCOUNTS National Competition Countdown Round, Mathletes had to solve each problem within 45 seconds, without the aid of a calculator. Here are a few of our favorites. Can you solve these in 45 seconds or less without using a calculator?

A basketball player started the day with a shooting average of 0.250 for the season, meaning he had made 25% of his shots. After shooting five times without making a shot today, his average dropped to 0.240. How many shots has the player made so far this season? (Countdown #20)

Let x♦ = xx. What is the value of (2♦)♦? (Countdown #25)

The figure shows a region bounded by four congruent circular arcs of measure 270°, each with radius 3 inches. When the area of the entire region is expressed as a + bπ in2, what is the value of a + b? (Countdown #19)

What is the greatest prime factor of the sum 52013 + 52014 + 52015 + 52016? (Countdown #24)