mathschallenge.net logo

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

Only Show Problem