All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Cut chessboard (Posted on 2003-09-26) Difficulty: 3 of 5
I cut myself a rectangle out of a chessboard. (All cuts were along the square lines, so the rectangle has integer sides.)

Were I to tell you either its area, or its perimeter, or the length of its diagonal, you wouldn't be able to determine the dimensions of the rectangle.

What's its size?

See The Solution Submitted by Federico Kereki    
Rating: 4.0000 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution the Solution | Comment 3 of 6 |
The way I did this was to run a small program to find all the possible diagonals from cut rectangles:

OPEN "cutchess.txt" FOR OUTPUT AS #1
FOR i = 1 TO 8
 FOR j = i TO 8
  PRINT #1, SQR(i * i + j * j), i, j

The output was then sorted by diagonal length, and it was found that only 7.07106 and 8.062257 were shared by more than one pair of dimensions: the former by 1x7 and 5x5 and the latter by 1x8 and 4x7.

All of these have non-unique perimeters, so perimeter doesn't narrow it down any further.

But 1x7 has a unique area as 7 is prime. Likewise 5 is prime, so the only other way to get 25 would be 1x25 and the chessboard is not that big. The 28 area from 4x7 is also unique, as the only alternatives, 1x28 and 2x14 are too big for the chessboard.

That leaves 1x8 as having the only ambiguous area as area 8 can also be 2x4.

So the answer is 1x8.
  Posted by Charlie on 2003-09-26 10:03:32
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information