Box Marking

Box Marking is the second of three phases of Sysudoku Basic. It follows the slink marking bypass, with the task of posting to the grid two sets of candidates: box slinks and aligned triples.

Box Marking is the second of three phases of Sysudoku Basic. It follows the slink marking bypass, with the tIn the bypass, aligned box slinks and aligned triples are major tools limiting placements in boxes. In box marking, we mark them for use in advanced solving. In doing so, we often spot combinations of pencil marks that imply more clues, and more slinks, etc.ask of posting to the grid two sets of candidates: box slinks and aligned triples.

In the bypass, aligned box slinks and aligned triples are major tools limiting placements in boxes. In box marking, we mark them for use in advanced solving. In doing so, we often spot combinations of pencil marks that imply more clues, and more slinks, etc..

Box slinks are pairs of candidates of the same number which form a strong link because they are known to be the only candidates of their number in the box. They are posted as pencil marks in the same position at the top of two cells of their box.

Aligned triples are sets of three candidates known to be the only three of the same number in the box, and occupying the three cells of a line intersecting the box.  If the line is a row, the pencil marks are placed at the middle bottom edge of the cell. If a column, they go on the middle right edge of the cell.

Row slinks, column slinks, and other non-slink candidates are identified in the line marking process following box marking.

The slink marking form of pencil marking is, as of this writing, unique to Sysudoku and sysudokies. The predominant, redundant, and ultimately distracting keypad pencil marking is indefensible  by comparison, and should have been retired by Sudoku writers long ago.

To illustrate box marking, here is the almost completed box marking of review puzzle II-49 from Sudoku Road to Mastery, by Moito Publishing.  Bypass gained only the clue E4 and the unresolved 3-fill c5[135].

For the “1:” list of the box marking trace shown below, a box slink is marked in NE and an aligned triple in C. They are recorded as NEm and Ct. The number is left out for markings of the list number.

In the 9: list, the second slink S9m combines with the previously marked S6m on the 6: list to form a naked pair to start a collapse.

It’s an instance of  systematic box marking revealing something missed in the bypass.

Aligned box slinks are also line slinks in the aligned direction. Since the two candidates are the only two of that number in the box, one of them must be true. That also means there can be no other candidates of that number in the entire line. That makes a box slink also a line slink, and it sweeps the two other boxes the line crosses as as well as a clue. 

 Since  the cells of an aligned triple contain the only three candidates of that number in the box, one of those candidates must be true. Like the aligned slink, the aligned triple sweeps the line of other candidates of its number.

Going back to the original grid, you can verify that the naked pair S69 that starts a collapse near the end of box marking could have been discovered in the bypass, if you kept the S6m in mind as you imagine N9m and S9m. But you might not have gained anything, unless you remembered all of the slinks of the grid above. The slink marks move the cause and effect navigation along, because whenever a candidate is proved false and eliminated, all of its slink partners are true.

Would you like to check out this effect by reading the trace of the collapse? Good. I just happen to have it.

On the last leg down, Wht257 refers to the hidden triple in the W box. The box slinks fix candidates of four numbers on 4 cells. But three of those numbers are confined to three cells. It means that those three cells must hold 2, 5 and 7 in the solution, and 3 cannot be in r4c1, and must go into r4c3.

The example shows that slink marking can generate hidden subsets as well as naked ones, like the naked pairs SW48 and S69. The subset cells are “naked”, when no extra candidates are in the set. The four cells marked in W are a naked quad, because the only missing number, 9, cannot go into r4c2.  The quad then locks it out of r5c1. It is also locked out of the three cells of the hidden triple.

Many times, box marking is simply routine preparation for line marking and advanced methods. But like this Moito example shows, box marking can rout puzzles in interesting ways. There’s a reason why the Sysudoku blog promotes desktop templates for Sysudoku Basic, but not software to display all number scanned candidates. Aren’t such adventures as these the purpose of Sudoku? 

 

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