The 26x36 Solution


Here's how the final test problem was constructed.  No
complaints are allowed, for the POTM-Master is omnipotent.

1. I wanted a large number of squares ... a smaller problem
	increases the likelihood of ties which I always
	strive to avoid.

2. I wanted to be sure there was a solution that used most
	of the squares for the same reasons.  
	In retrospect, It would have been hard to avoid having
	a large solution - but perhaps that's the subject of
	another POTM!

3. So.  I constructed a quilt with the word POTM in it
	(written in black on a white background in very
	jagged lettering).  It so happened that the quilt
	was 36 squares wide by 26 tall for a total of 936.

4. Then I took the white edges of the 936 squares and 
	randomly assigned colors to them so that they
	would continue to fit together.

5. Just for fun, I added 25 more squares - each of which
	was a single color - thus arriving at a total of
	961 squares to work with.  (Coincidentally, 31*31
	is 961, but I have no idea if such a quilt is
	possible as I'm writing this on 11/24/98!)

6. Next step was to randomize the rotations.  I decided to
	leave them in the original order since it was a
	pain in the neck to "shuffle" them.  As a result,
	the 36x26 solution I started with uses the squares
	in order from 1 to 936.

Well ... that's about it ... I wondered if there's anything
better than the 36x26 solution buried in the squares!!!

	SIZE	AREA	PERM	AREA/PERM
	31x31	961	124	7.75
	32x30	960	124	7.7419
	33x29	957	124	7.7177
	34x28	952	124	7.6774
	35x27	945	124	7.621
	31x30	930	122	7.62
	32x29	928	122	7.6066
	36x26	936	124	7.5484	(as constructed)
	30x30	900	120	7.50

	29x30	870	118	7.37...	(best found)













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