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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
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