## Shaded Grid

#### Problem

By only shading whole squares and given that is considered different to , how many different ways can a 2x2 grid be shaded?

#### Solution

Consider the following diagrams.

Therefore the number of possible ways to shade a 2x2 square is

1 + 4 + 6 + 4 + 1 = 16.

What about other sized grids?

Hint: Consider the total number of squares making up the grid and don't just think about square grids; a square is either shaded or not shaded... ;)

What if you used three colours: white, grey and black?Can you generalise for any size grid and any number of colours?

Problem ID: 86 (Nov 2002) Difficulty: 1 Star