Tiling with rectangles

A tiling with rectangles is a tiling which uses rectangles as its parts.

Tilings with non-congruent rectangles

The smallest square that can be cut into (m x n) rectangles, such that all m and n are different integers, is the 11 x 11 square, and the tiling uses five rectangles¹.
The smallest rectangle that can be cut into (m x n) rectangles, such that all m and n are different integers, is the 9 x 13 rectangle, and the tiling uses five rectangles¹.

See also

tessellation, tiling puzzle

References

1. Journal of Recreational Mathematics, 28:1, p.64.