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The number of ways in which the squares of a 8×8 chess board can be painted red or blue so that each 2×2 square has two red and two blue square is
A. 29
B. 291
C. 292
D. None of these.

Answer
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Hint: First we will draw a normal 8×8 chess board which has 8 rows and 8 columns. This means that there are a total 64 small squares but we have to choose a 2×2 square. As we know that to color m×n chess board there are 2m+2n2 possible ways. So, we use this to find a correct answer.

Complete step-by-step answer:
First we draw a diagram of a chess board with 8 rows and 8 columns.
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We have to paint it red or blue so that each 2×2 square has two red and two blue squares.
As we know that t to color m×n chess board there are 2m+2n2 possible ways.
We have a 8×8 chess board, so the possible ways to color it will be 28+282
When we solve this equation we get 2.282
As we know that am.an=am+n
So the equation becomes 292
So the total number of ways the squares of a 8×8 chess board can be painted red or blue so that each 2×2 square has two red and two blue squares is 292 .
Option C is the correct answer.

Note: The key factor in this question is that a student knows the number of rows and columns of the chess board. Also, by drawing the diagram things get clearer to students. The possibility of mistake can be in solving the equation 28+282 . Some students can add the powers as 2162 . So keep the point in mind while solving the equation.
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