This post describes an adaptation of Sysudoku box marking which is suitable for timed solving contests. I call it the slink marking bypass. You apply the slink and triple marks to finding clues and cell claiming naked pairs only, bypassing the writing of other pencil marks. Here it is illustrated and compared with the Gordon Guide “scanning”, and with full box marking, on the example that introduced “scanning” in the Guide.
I’ve gladly admitted, after each of the Akron-Summit County Library Sudoku tournaments, to be nowhere close to being a contender. Of course my tender age of 76 may have something to do with that, but another telling factor is that only clues count, not pencil marks. In the Akron tournament in fact, all pencil marks that are put in must be erased. Going through my Sysudoku traces of the championship puzzles, you can see what a great excuse that is.
You know that this blog is directed at human solving of the toughest Sudoku, but even the championship puzzle of many timed contests are basic level. They never make it to the advanced techniques that require pencil marks. If we expect a basic level puzzle, why not just bypass candidate pencil marks? Or at least, put them off until they are easier to do, and there are fewer of them. In a timed contest we won’t be tracing or reading a trace, but I’m including traces so you can “read” in a 2-D trace how fast the dublex bypass would be.
Gordon’s “scanning” and Paul Stevens’ similar “cross-hatching” incorporate the dublex, or double line exclusion. Let’s examine Example 3 of the Gordon’s Guide. Peter scans numbers in order, 1 – 9. In the Guide he does a few scans out of order to begin his discussion, but we’ll go by his regular order, for a better comparison.
Here is the grid after scanning 1 – 5 :
The trace is in the 2-D format. For this introduction only I’m adding cause coding:
h – horizontal dublex, v – vertical, oc – one-choice. Cause and effect is shown by indenting, and ordering is 2-D style, i.e. depth first.
Note that NE5 triggers NE4, but SW8 does not generate SE8. That is because 4 was an earlier scan, but 8 is a later one. The dublex scan will be depth first regardless, following each cause as far as it goes.
Also note that the r7 fill is not made when SW5 reduces free cells to two. That is a speedup feature of the slink marking bypass.
Gordon says “Whenever I put in a number using horizontal scanning, I like to immediately look vertically to see if that gave me enough information to make a conclusion based on vertical scanning.” Actually his marking is stronger than that. His SEhv2 requires a simultaneous cross hatch. Neither the horizontal or vertical scan would do it alone. What Gordon actually does is box marking for clues only, less slink marking, and two-cell fills.
The Cnr1 is a surprise for Guide readers. I’m coding it as “nr”, for “new rule”. The clue could have been traced as Cv1, but Gordon uses it to call attention to his number closeout procedure.
He mentioned before that he notes when 9 clues of a number has been found, so that he will not have to consider the number again. But he also notes when the eighth clue shows up, because then the location of the final number is known. Its row and column are the only ones missing the number.
Let’s think about that.
Do we agree that it isn’t really necessary to track numbers of clues to do this? The two clues in the horizontal and vertical to cross hatch the last clue have to be there when the count reaches 8.
With scans left pending, Peter starts through the numbers again. His count tells him that two 2’s are missing and he accounts for them, but the counts and this accounting take time. At the 3’s, he finds Nh3, and uses the new rule for Cnr3, but we can see he simply missed Nv3 when he entered Soc3. He should look both ways after a one choice, as he does after a scan effect. And the Nh3 generates Cv3 without the new rule.
Next found is the Wv4. We look at the trace to see which came first, the W9 or the SW4. It’s the SW4, so Peter did not note that the W9 closes the Wc2 chute, and look for a vertical scan that might result. The correction brings in a pile of clues. In Gordon’s accounting we learn that he doesn’t regard the last number in a line as a one-choice.
The second traverse of the numbers goes to 7 before the puzzle is finished, but we have learned enough. The dublex scan will carry every effect clue as far as possible, using the same form of 2-D trace. Two free cells in a unit will be filled with clues or a naked pair, as soon as created. There is no second traverse of numbers.
Here is the grid after the dublex bypass on 1 – 3:
To the trace below, NE3 closes a second chute in the NE box, and NE5 takes away the alternative for NE4, leaving a “one-choice” for NE9. NW5 brings the first two cell fill, and NE9, the first naked pair fill.
Pencil marking the naked pair fills is optional, but I think it pays. Foregoing other pencil marks does concentrate the marking effort on clues.
It may delay the collapse, but in a timed contest, who cares?
The grid at Cnp46, along with the tail of the trace, shows how the pencil marks can speed up recognition of the last few clues of the collapse.
Adding to the success of the bypass, I can report that a full slink marking of this puzzle does no better, and undoubtedly takes more time.
The Guide example was certain to show off the bypass well. You might want to evluate it against the Akron Tournament championship puzzles reported here in November 2012 and 2013. I will suggest and do more such evaluation ahead.
Compare traces with me. I think you’ll find full slink marking necessary, but start with the bypass, and see how far you can go. Then do box marking. Enjoy.