# A Description Of The Problem Solving Report Essay

Solution to the Problem:

I found there are 100 rectangles in a 4x4 grid.

General Problem:

(n^2 〖(n+1)〗^2)/4

Strategies to Finding the Solution: Once I understood what the question was asking, I tried to figure different methods that would simplify the problem. The first method that I thought of was finding how many rectangles in a 1x1 grid, 2x2 grid, and a 3x3 grid. The first grid that I worked with was the 1x1 grid because it seemed to be the easiest.

When doing the 1x1 grid all I had to do was briefly look at the grid and I knew there was only one rectangle. After figuring out how many rectangles were in a 1x1 grid I moved onto the 2x2 grid. However, this time I could not briefly look at the grid and know how many rectangles there were. This time when counting the squares I decided that I was going to label each square in the 2x2 grid, like the grid below. Now with the entire 2x2 gird labeled I could give each rectangle I found a…