Find a dissection of a 19x19x19 cube such that all the pieces are cubes with integer dimension and none of them are unit cubes.
(In reply to
re: first observations by Jer)
Here is one dissection of a 19x19 square into non-unit squares:
Place a 13x13 square in the top left corner and a 6x6 in the lower right. This leaves two 6x13 rectangles.
Place two 3X3 rectangles along the remainder of the left edge and two along the remainder of the top edge. This leaves two 6x10 rectangles which can be tiled using 2x2 squares.
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Similarly, I can put a 9X9 in the top left corner and a 10X10 in the lower right. Place two 5X5 rectangles along the remainder of the left edge and two along the remainder of the top edge. This leaves two 4x10 rectangles which can be tiled using 2x2 squares.
Edited on June 13, 2015, 8:10 pm
re(2): first observations
