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.

26^2-1=27*25.

45 3x5 rectangles exactly cover the 27*25 rectangle, so at least 46 are needed to cover the larger area. The missing strip of area 1x26 can be covered with 6 rectangles placed along their long sides, so no more than 45+6=51 are needed.

Posted by broll on 2011-06-23 12:15:01