biG wrote:Playing with Grids - From First to Last
Definitions
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Grids
I copied the grids from my RefPOST (refer to my Defintions) into a text editor and edited them to create these grids.
- Code: Select all
c1 = 1 2 3 4 5 6 7 8 9 c1 = 1 2 3 4 5 6 7 8 9
.---------.---------.---------. .---------.---------.---------.
r1 | 1 2 3 | 4 5 6 | 7 8 9 | r1 | 9 8 7 | 6 5 4 | 3 2 1 |
r2 | 4 5 6 | 7 8 9 | 1 2 3 | r2 | 6 5 4 | 3 2 1 | 9 8 7 |
r3 | 7 8 9 | 1 2 3 | 4 5 6 | r3 | 3 2 1 | 9 8 7 | 6 5 4 |
:---------+---------+---------: :---------+---------+---------:
r4 | 2 1 4 | 3 6 5 | 8 9 7 | r4 | 8 9 6 | 7 4 5 | 2 1 3 |
r5 | 3 6 5 | 8 9 7 | 2 1 4 | r5 | 7 4 5 | 2 1 3 | 8 9 6 |
r6 | 8 9 7 | 2 1 4 | 3 6 5 | r6 | 2 1 3 | 8 9 6 | 7 4 5 |
:---------+---------+---------: :---------+---------+---------:
r7 | 5 3 1 | 6 4 2 | 9 7 8 | r7 | 5 7 9 | 4 6 8 | 1 3 2 |
r8 | 6 4 2 | 9 7 8 | 5 3 1 | r8.| 4 6 8 | 1 3 2 | 5 7 9 |
r9 | 9 7 8 | 5 3 1 | 6 4 2 | r9 | 1 3 2 | 5 7 9 | 4 6 8 |
'---------'---------'---------' '---------'---------'---------'
A114288 (first minlex) A112454 (last minlex)
c1 = 1 2 3 4 5 6 7 8 9 c1 = 1 2 3 4 5 6 7 8 9
.---------.---------.---------. .---------.---------.---------.
r1 | 2 3 | 5 6 | | r1 | | | |
r2 | 4 5 6 | 7 8 9 | | r2 | B1 | B2 | B3 |
r3 | 7 8 9 | 1 2 3 | | r3 | | | |
:---------+---------+---------: :---------+---------+---------:
r4 | 1 4 | | 8 9 7 | r4 | | | |
r5 | 3 6 5 | | 2 1 4 | r5 | B4 | B5 | B6 |
r6 | 8 9 7 | | 3 6 | r6 | | | |
:---------+---------+---------: :---------+---------+---------:
r7 | | 6 4 2 | 9 7 8 | r7 | | | |
r8 | | 9 7 8 | 5 3 1 | r8.| B7 | B8 | B9 |
r9 | | 5 3 | 6 4 | r9 | | | |
'---------'---------'---------' '---------'---------'---------'
"The 48" (33 holes) Block Numbering
Alternative Block Numbering
-------------------------------
B1 = B1-11, B2=B-12, B3=B-13
B4 = B4-21, B5=B-22, B6=B-23
B5 = B7-31, B8=B-32, B9=B-33
c1 = 1 2 3 4 5 6 7 8 9 c1 = 1 2 3 4 5 6 7 8 9
.---------.---------.---------. .---------.---------.---------.
r1 | 1 2 3 | 4 5 6 | | r1 | . . . | . . . | . . . |
r2 | 4 5 6 | 7 8 9 | | r2 | . . . | . . . | . . . |
r3 | 7 8 9 | 1 2 3 | | r3 | . . . | . . . | . . . |
:---------+---------+---------: :---------+---------+---------:
r4 | 2 1 4 | | 8 9 7 | r4 | . . . | . . . | . . . |
r5 | 3 6 5 | | 2 1 4 | r5 | . . . | . , . | . . . |
r6 | 8 9 7 | | 3 6 5 | r6 | . . . | . . . | . . . |
:---------+---------+---------: :---------+---------+---------:
r7 | | 6 4 2 | 9 7 8 | r7 | . . . | . . . | . . . |
r8 | | 9 7 8 | 5 3 1 | r8.| . , . | . . . | . . . |
r9 | | 5 3 1 | 6 4 2 | r9 | . . . | . . . | . . . |
'---------'---------'---------' '---------'---------'---------'
"The 54" (27 holes) Next?
My idea was to demonstrate the 48-char compression with a specific example. Start with the minimum minlex grid. Since we are documenting, lets draw the maximal minlex grid beside it. Observe as we go.
The first thing I notice is that the first grid A114288 could be transformed into that last grid A112454 in a modulo-10 sense. E.G. iterating into the values of the fisrt grid: subtract the value from 10 and that was the value for the last grid. Made me go "hmmm..." Seems like there is a symmetry here. Could I just "calculate" the first ED/2# grids and generate the last half by applying modulo-10 operations. My gut - feeling says the last half of the ED is geneated from the end to the middle. What say you?
Then in the process of decompressing The 48 grid by doing a "full house" on six blocks produces The 54" grid. Of course by experience I "know" the grid can be solved from there to the full 81-char puzzle. However, I was still wanting to see this visually in some way. It made me think of that so-called SET (Set Equivalence Theory) method again! Where do I go now?
