Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

Consider the six by six grid of unit squares below. How many rectangles of area 8 square units can be formed using only the line segments of the grid as the sides of the rectangles?

problem
Solution
There are only two kinds of rectangles of area 8 square units which we can form on the grid: rectangles and rectangles. For rectangles, the upper left unit square of the rectangle must be in the left three columns and top five rows, giving 15 possible locations. Similarly, there are 15 possible locations for a rectangle. Therefore, the total number of rectangles of area 8 which can be formed is .
Final answer
30