Question

In how many ways we can select the two adjacent squares in a chess board.

Answer 1

Answer:

This problem probably has many solutions but I'm going to do it with recursion

It is obvious (by counting) that you can select 4 adjacent pairs of squares in a 2x2 chess board. Now if you add in a L-shaped to make it a 3x3:

LOO

LOO

L L L

There are 2(n-1) ways to select adjacent pairs among the L's only. And there are also 2(n-1) ways to connect the L's and the O's as adjacent pairs. So, if a_n represents the number of ways to select adjacent squares in a n by n board, then:

a_n = a_(n-1) + 4(n-1)

by recursion, a_8 = a_2 + 4(2+3+4+5+6+7) = 112.

Please mark as Brainliest.

Answer 2

Step-by-step explanation:

1 x 5 squares = 4 * 8 = 32. 1 x 6 rectangles = 3 * 8 = 24. 1 x 7 squares = 2 * 8 = 16.