If you were told to draw a rectangle along the lines of a sheet of graph paper such that its area is 40 squares, you could choose rectangles measuring 8x5, 10x4, 20x2 or 40x1.

For two of these, 8x5 or 10x4, you would find that you could draw a diagonal across the rectangle that would pass through exactly 12 squares.

What is the smallest number of squares that could be the area of three different rectangles whose diagonals pass through the same number of squares? How many squares does this diagonal pass through?

Computer-aided progam does help in solving the problem.  However, the program is rigid and it is from human brain.  As it is from human brain, it is subject to human error.  Any human mistakes in the designing of computer-aided program would not help to solve the problem.  Computer is simply like garbage in garbage out.  It is the same as any computer virus goes into the computer, virus will be its product so much so it could not function properly.

This is the gentle words from me.  If the answer is one square, it is not a rectangle but a square.  As the question requires the answer as a rectangle, the answer could never be a square.

Thus, there is an open discussion for this question since it has not come to the right answer yet.

Thanks.

Edited on April 28, 2005, 5:10 am

Posted by Jonathan Chang on 2005-04-28 05:08:45