Rook blockage

Probability Level 4

How many squares, of any size, which don't contain a rook, are there in this board?


The answer is 128.

Rama Devi by Rama Devi , 43, India

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1 solution

Rama Devi
Jun 16, 2015

128.

There are 62 squares of size 1x1.

There are 41 squares of size 2x2.

There are 18 squares of size 3x3.

There are 6 squares of size 4x4.

There is 1 square of size 5x5.

A total of 62 + 41 + 18 + 6 + 1 = 128.

Please up vote if you like it .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

How did you get the numbers 62, 41, 18, 6, 1?

@challenge master note :

In the case of 1 x 1 squares , two squares contain a rook.Therefore there are only 62 square without a rook.

In the case of 2 x 2 squares , 8 squares contain a rook.Therefore the number of squares is (49-8),which is equal to 41.

In the case of 3 x 3 squares , 18 squares contain a rook.Therefore the number of squares is (36-18) , which is equal to 18.

In the case of 4 x 4 squares , there are 19 squares which contain a rook.Therefore the number of squares is (25-19) , which is equal to 6.

In the case of 5 x 5 squares,the number of containing a rook is 15.Therefore the number of squares which do not contain a rook is (16-15),which is equal to 1.

Please up vote if you like this solution.

Rama Devi - 5 years, 12 months ago

Its a good solution ma'am.

Sai Ram - 5 years, 12 months ago

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