2016 AMC 10B Problems/Problem 14
Problem
How many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line , the line and the line
Solution
The vertical line is just to the right of x=5, the horizontal line is just under y=0, and the sloped line will always be above the y value of 3x. This means they will always miss being on a coordinate with integer coordinates. After counting the number of 1x1, 2x2, 3x3, squares and getting 30, 15, and 5 respectively, and we end up with
Solution by Wwang