Geometry with Chessboards

Geometry Level 3

The above figure is a piece of chessboard. Which area is the larger area, white or black?

White Can’t be determined. Black=White Black

Hana Wehbi by Hana Wehbi , 51, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

The given image when rotated by 18 0 o 180^o and merged with itself gives us a 5 × 7 5\times 7 grid.

This grid as seen above has 35 35 squares, 18 18 black and 17 17 white. Since the original image is exactly half of the above grid it contains half of each of the type of squares.

Thus the original image has 9 9 black squares and 8 1 2 8\dfrac{1}{2} white squares.

So the black area is larger.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Observed that the three vertices of the triangle are all colored black (encircled red in my figure). Therefore, black has a greater area. This conclusion is accepted since the squares of a chessboard are equal, and the white and the black squares are alternating.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

A chessboard is 8 x 8 and has an equal number of black and white squares, 32 of each. The shown figure is indeed a “piece of chessboard,” but ranks 6, 7 and 8 and file h are not shown.

Steven Adler - 4 months, 2 weeks ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...