How many 3x5 rectangles are necessary to fully cover a 26x26 square?
Clearly, overlapping each other and/or the edges of the square is allowed.

Note that 26x26 divided by 3x5 gives 1 remainder, so it's worth asking, is there a configuration that leaves this 1 remainder?

In fact there is. If you cover the top left area with a 20x21 rectangle, the top right with a 21x5 rectangle, the bottom right with a 5x6 rectangle, and the bottom left with a 6x20 rectangle, there will be one square missing. Thus, simply covering that square with an extra piece will finish the covering.

(Edit: now the area is covered with "rectangles")

Edited on June 25, 2011, 2:35 pm

Posted by Gamer on 2011-06-25 01:45:40