Question

Consider a grid as shown in figure having 8 blocks of dimension 1 x 1. Each block is to be painted with either blue or red colour. In how many ways this can be done if at least one block of dimension 2 x 2 is to be painted red completely?

• A. 37
• B. 36
• C. 39
• D. 40

Answer 1

The correct option is C 39

At least one block of dimension 2 x 2 is to be painted red completely

So, we have to paint red any 2$\times$ 2 grid first

so therefore no. of ways will be $3\times 2^4=48$

It will have some repeated elements too. when two (from diagram) $2\times 2$ terms will be shaded red i.e.(2^2+2^2 +2^1) ((1),(2),(3))

And also it will have 1 term when all shaded red (4)

$\therefore 48-10+1=39$

Answer