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 Competition

Click here to download the problem.

Congratulations to all the Mathletes who made it to the 2013 Raytheon MATHCOUNTS National Competition, and especially to the winners! Here are just a few of the problems competitors had to solve.

A large quadrilateral is divided into four smaller non-congruent regions, and each region is painted with a different color. The possible colors are red, blue, green and yellow. One possible way to paint the quadrilateral is shown below. Including the way shown, how many total ways could the quadrilateral be painted? (Sprint #6)

A set contains four integers. The sums of the integers in each of its three-element subsets are 82, 88, 79 and 84. What is the median of the original set of four distinct integers? (Target #3)

Eight-letter permutations can be made by using four letters from the word MAINE and four letters from IDAHO. How many unique eight-letter permutations are there? (Team #3)