A square is subdivided into 9 smaller squares of equal size. If each o

Question

A square is subdivided into  9  smaller squares of equal size. If each of these smaller squares will be painted either red or green, in how many ways could these smaller squares be painted if two adjacent squares in the same row cannot be painted using the same color?

A) 2

B) 8

C) 12

D) 72

E) 512

ashikjoshy · Answer

For each row, we need to consider the color to be painted. For say e.g, for the first row suppose we select the first square to be painted, the we have two possible options to choose. Similarly, moving towards the second square in the same row, we will only be left with a single option as we cannot paint the same color in adjacent squares. Hence, for each row we have only 2 possible ways to paint the squares in a row. This permuted for all the three rows, we will have the answer as 2*2*2 = 8.

Hope this helps !!

Hope this helps !!

Moonlion · Answer

When a square is divided into 9 equal parts, then there will be 3 squares in a row and similarly 3 squares in a column. In total there will be three rows and three columns with 3 squares in each row.

Now, consider taking first row. Let then name A, B, C in order. No. of ways to paint A will 2!. No.of Ways to paint B will be 1 only since adjacent square can't be of same colour. Similarly, No. of ways to paint C will be 1. Hence, No. of ways to paint first row squares will be 2! x 1 x1= 2!. Since there are three rows, total no. of ways to paint all 9 squares will be 2! x 2! x 2!= 8.
Hence, option B is the correct answer.

Fdambro294 · Answer

3 square in 3 rows.

Since the only constraint is that any 2 adjacent squares in a given row can not have the same color, for any given row we have 2 available options:

Red - Green - Red

Or

Green - red - green

We can mix and match the 2 options in row 1 with the 2 options in row 2 with the 2 options in row 3

(2) (2) (2) = 8 ways

Posted from my mobile device

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A square is subdivided into 9 smaller squares of equal size. If each o

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