Yes, this is the solution I had in mind. The rhombus is actually a square. Jim Propp On Saturday, July 7, 2018, Fred Lunnon <fred.lunnon@gmail.com> wrote:
OK then, how about one 1x1 and one 2x2 tile in a rhombus: ^ / + \ / + + + \ \ + + + / \ + / v
I think the answer to the second question may well be no: the vague reason being that the space between the two larger tiles cannot be filled by the smallest without repetition?
WFL
On 7/7/18, James Propp <jamespropp@gmail.com> wrote:
No, I meant two squares of unequal sizes.
Jim
On Saturday, July 7, 2018, Fred Lunnon <fred.lunnon@gmail.com> wrote:
And did you mean "squares of two unequal sizes" ? WFL
On 7/7/18, James Propp <jamespropp@gmail.com> wrote:
Oops; I just realized that a “squared square” is an answer to the question as asked!
I meant to specify (in both the puzzle and the question) that the tiling must not have points where the corners of four squares meet.
Jim Propp
On Saturday, July 7, 2018, James Propp <jamespropp@gmail.com> wrote:
Inspired by Scott Kim’s work on motley dissections ( http://www.gathering4gardner.org/g4g13-videos/), I offer a puzzle that I know the answer to and ask a question I don’t know the answer to:
Puzzle: Find a tiling of the square torus by two squares of unequal sizes.
Question: Is there a tiling of some (not necessarily square) torus by more than two squares, all of unequal sizes?
Jim Propp
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