On 2019-05-21 11:20, Mike Stay wrote:
How is that different from a tight packing on a slightly smaller paper with slightly larger squares?
In at least one way: In the "quarter inch spacing" model, two adjacent squares in a single pentomino don't have the larger distance.
On Tue, May 21, 2019 at 12:17 PM Scott Kim <scottekim1@gmail.com> wrote:
Here's a new type of polyomino problem that came up as a practical problem.
Fit the twelve pentominoes, each made of 1" squares, on a standard 8.5" by 11" sheet, so there is at least a 1/4" border between every pentomino and its neighbors, and the edge of the paper. In other words, pentominoes never touch each other, or the border of the paper. Note that given the spacing constraint, no pentomino is allowed to be inside the concave space of the U pentomino.
It's easy to fit 11 pieces, but 12 is challenging. It should be fairly straightforward to write a solver, but the loose fitting constraint does make things trickier. I did a find a solution by hand...which cannot be compressed to fit on a smaller sheet. The next question is what is the smallest area that can fit all 12 pentominoes with quarter inch spacing? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun