Countdown to Victory

May 18, 2015

See if you can solve the winning question plus two others that stumped the champion and runner-up in the Countdown Round at the 2015 Raytheon MATHCOUNTS National Competition. Remember Mathletes® are given only 45 seconds to answer these questions!

How many arithmetic progressions of six increasing terms include the terms 15 and 20?

 

A T-shaped figure is made by arranging four squares of side length 4 cm as shown. In centimeters, what is the circumference of the largest circle that fits within the boundary of the T-shaped figure? Express your answer in terms of π.

 

What is the least positive integer n for which the sum of the first n positive integers is divisible by 100?