**Number Squares Chess Board Teaser - 28 November**

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks.

How many are there?

**For Solution :**Click Here

Duh, 62?

ReplyDelete124 or more

ReplyDeleteInteresting puzzle.

ReplyDeleteAll squares of a chessboard are: Σ(n=0 to 8)n^2=204

That is 8*8+7*7+...+2*2+1*1=204.

The easy way to do it is to subtract the squares with a rook from each "class" of squares.

Squares of order 1. 1X1 = -2 (1 for each rook)

Sq. of order 2X2 = -8. 4 for each rook (imagine the rook at every square of 2X2=4 possible)

Sq. 3X3 =9 +9=18

Sq. 4X4 : 1st rook(at f3) =16-6 (down)=10

2nd rook (at d6)=16-6-1 (the square which contains the other rook)=9

Sq. 5X5 :from 16 total remains only 1 thus -15

Sq. 6X6, remains none --- -9

Sq. 7X7 none remains ---- -4

Sq. 8X8 none ---------------- -1

TOTAL REMAIN: 204-2-8-18-10-9-4-1= 152 squares that do not contain a rook.

There are 36 squares available for the other two rooks to be placed, so 34 squares don't have rooks.

ReplyDelete36

ReplyDelete62

ReplyDeleteThe right answer ist 128

ReplyDelete62 + (49-8) + (36-18) + (25-19) + 1