Sunday, October 3, 2021

Sudoku Musing

A SUDOKU MUSING

One of the things I'm a little bit proud of in my journey of sorting out how to solve Sudoku puzzles is that I've never looked for any advice. Early on I wrote some VBA code to quickly get past the easy 'giveaway' answers, which was fun in itself, but since then I've only relied on methods and rules I've come up with or set for myself. Neither am I a master of it by any stretch of the imagination, I make a lot of stupid mistakes and keep getting the feeling that I'm missing something in my logical analysis, hoping that another revelation or strategy will appear.

To start with I like the simple approach, it's either this or it's that, binary if you will. However I've not yet got a foolproof notation of such which I think leads to misinterpreting my notes. After the Excel VBA phase I decided that too many notes were not helping me, a cluttered grid gets in the way. In a row, column or square of 9 I'll note two possible places for a number (which I'm thinking sometimes gets me into trouble). More reliable, I think, is determining that a given cell can only be one of two numbers, so I'll note that too. I don't want the clutter of more than two possibilities happening for a given cell, although that still happens sometimes with my current approach.

But that's not what I wanted to talk about here. There's a pattern I've seen but have not yet drawn any conclusions from, so I thought I'd walk through where I am at the moment then see how this particular example plays out in hopes of learning something. So let us start with the 5-star puzzle ("by Dave Green") presented in the Akron Beacon Journal, Sunday October 3, 2021.

In order to discuss this, I'll need a way of identifying cells.  I'm sure folks have come up with their own ways of talking about this but as with all other things Sudoku thus far, I'm doggedly blazing my own way. The first and perhaps simplest approach that came to mind was simply to ID each cell by row and column, AA through II.  This pays no regard to squares of 9. That would work but...

I like this second approach that came to me. Each square-of-9 (call it a GROUP) will be identified with a letter A through I. Each cell within a group will be identified in the same way with a second letter. Rightly or wrongly I thought that might steer us/me through the grid faster. As with the first ID approach, the very top left cell would be AA, but now the fourth cell in the top row becomes BA. 



Thus, in the puzzle presented below (Oct. 3 five-star): cell AB=9; CA=2; CC=4 and so on. (Note to self: in Paint.net the bigger numbers are calibri 20 bold, notes are 10 not bold.)


I started solving the easy bits as follows with my entries in green & notes in red:

This is where it gets interesting with the eights. In group C there are a solid pair, solid in that within both that group and entire row it's one cell or the other has to be an eight. Proving or disproving either one will have immediate result. The same can be said of the eights in group H. 
Less solid are the two eights in the last row, they're a valid pair in that the logic is good for that entire row, but because they're in different groups I might be deceived. The problem is that within group I the two potential eights I've identified so far aren't the only candidates. Cell IA might be an eight, I don't know yet. If IA was shown not to have "eight potential" that would lock the other eights in. Proving any one of them would toggle all the rest of those eights on or off.

I'll watch what happens, but even if IA turns out not to be an eight I won't really know if this is a pattern I can 'take to the bank', it might just be in this instance.

A little later, not getting very far but here's another yellow-liner that makes me wonder if it's safe to assume these are my good choices for fives. There are no super-solid pairs as the semi-solid pairs (dashed lines) are in rows or columns but not within groups. The dotted lines connect questionable pairs, each groups involved has another possible five that I've not noted.

If this pans out, be sure to notify Oslo.

Summary: If I can trust these associations and infer that the questionable cells don't contain those fives and eights then maybe I can move ahead. Otherwise I'm a bit stuck at the moment. 
Below see the questionable cells: orange for cells I'm going to presume are NOT five; purple for the cell I'll presume is NOT an eight (IA).

Two days later I'm still stuck, BUT I think I proved that putting a five in any of those orange cells would result in problems for the fives. Not so much luck with the eights. Neither could I get anywhere along those lines with the sixes. 
Maybe it's time to erase the whole thing and start over, perhaps I made a mistake somewhere. Doh!