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

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)

## Problem Resources

Current Problem of the Week

Problem of the Week Archive

Past Competitions

Poster Problem Archive

MATHCOUNTS Errata