+1 vote
909 views
by (67 points)
1)2^9

2)2^9-1

3)2^9-2

4)none of these

Please log in or register to answer this question.

1 Answer

0 votes
by (64.2k points)

Solution:

For an m×n chessboard there are 2m+2n−2 ways.

Case I. There are two horizontally adjacent squares of the same color: 2m−2 ways.

Case II. There are two vertically adjacent squares of the same color: 2n−2 ways.

Case III. None of the above: 2 ways.

Hint for Case I: There are 2m−2 ways to color one row so that two adjacent squares have the same color. 

The rest of the coloring is determined from that; colors must alternate in each column. (Note, therefore, that Cases I and II do not overlap.)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...