Question

The number of ways in which the squares of a $8\times 8$ chess board can be painted red or blue so that each $2\times 2$ square has two red and two blue square is

• A. $2^9$
• B. $2^9-1$
• C. $2^9-2$
• D. None of these

Answer 1

Answer: (C)

$2^9-2$

For $m\times n$ chess board
No. of ways $2^m+2^n-2$
We have $8\times 8$ chess board
$\therefore$ No. of ways each $2\times 2$ square has $2$ red and $2$ blue squares $=2^8+2^8-2$
$=2.2^8-2$
$=2^9-2$