Is it possible to find tiling of a square into an odd number of non-rectangular pieces each having identical shapes and the same area? (Regard a given piece as identical to another if the rotation and/or reflection of the first piece is identical to the second)
If so, provide an example. If not, prove that it canít be done.
(In reply to Solution
This tiling sounds tough to lay out at first. But it is not that hard with a good strategy.
Start with the L triomino and find any rectangle with odd dimensions it can tile. In this case 15 tile a 5x9 rectangle:
Then use the trivial tiling of 45 of these rectangles into a large 45x45 square, using 675 total L triominos
This process can also be applied to some of the pentominos. The L and P pentominos each tile a 7x15 rectangle, so they will each tile a 105x105 square using 2205 pentominos.
The Y pentomino tiles a 15x15 square
, and is likely the smallest square that satisfies the problem.
Edited on October 26, 2016, 10:50 am