This page will help you get started solving Sudoku puzzles and reading the blog, especially if you don’t have much experience with Sudoku. The early posts require no experience, but it helps to know in general how a puzzle is solved, and how to make the starting moves.
Like many strategic games, Sudoku solving is done by accumulating small advantages, filling in numbers (clues) when you become certain that they belong there. The beginning clues, the givens, define the puzzle. Along the way, you gradually decrease possible numbers, the candidates, that can occupy the cell in the solution. Of course, the solution is the placement of nine numbers so that every box and every line contains all nine numbers. Barring errors, the puzzle has one and only one solution.
Sudoku solving is naturally divided into two phases. The accumulation of candidates, basic solving, is followed, if the puzzle is that difficult, by advanced solving, where logical relationships between candidates are used to reduce candidates in each cell down to one. There is a wrong way to do this. Its to generate all possible candidates from the givens, and then begin eliminations. Sysudoku basic solving is much more efficient, and is therefore easier and much more fun. We accumulate candidates systematically to reduce the candidates already accumulated, keeping the puzzle grid as simple as possible.
Sysudoku basic solving itself takes two phases. The first, box marking, concentrates on boxes, the 3 by 3 cell blocks that divide the 9 by 9 grid of the puzzle. The second, line marking, fills in the remaining candidates line by line.
Here is how boxes and lines are named in Sysudoku. Boxes are named as compass direction from a center box C. Rows are numbered North to South, and columns, West to East.
In box marking, we use the fact that a line can contain only one copy of a number to eliminate that number from cells of a box. Lines can be coordinated to force a solution number in a cell of the box, in two ways:
The bread-and-butter move of box marking, the double line exclusion, or dublex. Lines across two boxes force a clue in a third box by confining the number to a third line running through the boxes. In the grid diagrams the script numbers are added clues. In this example, you see how a script font distinguishes givens from added clues.
Of course new clues join right in with the box marking, eliminating clues in other boxes.
The other box marking move is the crosshatch. Clues of the same number in two unaligned boxes sweep simultaneously into two boxes, banning clues of that number from cells of those boxes. Here, E (East) and SW (yes, SouthWest) 1’s sweep the W box, leaving only one cell for the W 1-clue, or as we name it in Sysudoku traces, W1. Where is W1?
Did I mention traces? Traces are records of the moves made to solve the puzzle. Efficient traces are the mark of a system designed for difficult, as well as easy Sudoku puzzles. In Sysudoku traces, space is saved by not saying why or exactly where in the box the change occurs. Instead, trace reader knows or figures out why the change occurs, and marks right box cell on the grid. In this case W1 goes into r6c1. Was that your answer?
The second crosshatch of these two 1’s in the SE box excludes four cells. But it leaves three possible cells for SE1. Not good enough for marking. We get to what is good enough below. Later, let’s say, a 1 is added in r9c5, which adds another clue. Where? Wait, wait, don’t tell me, in . . .
SE1. It’s a cross hatch with a dublex. Now, how many cells does that leave for C1? That’s good enough for marking. The reasons come up next.
In sysudokie box marking, we record particularly useful candidates along with clues, in the form of pencil marks. Pencil marks are smaller font digits that fit into the corners and sides of cells. They represent candidates of two kinds, box slinks and aligned triples. You don’t need to look up these terms on the Sudoku Speak. The following examples define them.
Here, two candidates are identified in the West box, by a dublex. A box slink is a set of exactly two candidates of a number in their box. Such a pair form a strong link, a fundamental entity in Sudoku. In Sysudoku we call them slinks, for short.
A slink is a logical entity. Now don’t panic. Sudoku logic is street wise, common sense, sand box logic. In Sudoku, a candidate can turn out to be true, meaning a clue in the solution, or false, meaning it is eliminated along the way. A strong link is defined by this: if one candidate is found to be false, the other must be true. The only two candidates for a number in a box are strongly linked, aren’t they? The box must contain that number.
So, why does being a slink make those two candidates important enough to be pencil marked? Well, a 2 in column c1, or c3 now generates a W2 clue. In the previous example, the 1-slink you identified has the same mission.
Slinks can also be box sweepers. Here, a slink generated by a crosshatch forms a dublex to generate the clue S6
Once you get well acquainted with box slinks, Sysudoku will carry its e clutter reduction campaign further, by introducing an early phase of box marking in which slinks like this one are noted mentally, but not written in immediately . It’s called the slink marking bypass.
Besides the slink, there is another pencil marked box sweeper, the aligned triple. Here, a new SE5 leaves only one line in S for 5’s, and that is pencil marked along the bottom of three cells.
Clearly, the aligned triple and clue form a dublex generating SW5.
Sysudoku calls the three cells common to a box and a line a chute. The aligned triple in chute Sr8 became possible when chute Sr9 was filled. A filled chute is sometimes called a wall. In box marking we take notice when a wall is filled, and look around to see what that might cause.
Here’s a few more newly formed box formations that cause blips on our clue radars.
A 2 by 2 square of clues creates slinks or clues from sweeps from either direction. Look along the passing row and column for clues or marks of numbers missing from the square.
A four-corner box of clues (below)creates marks in lines crossing the center cell. Two such clues in a line creates a naked pair, which excludes other numbers from these two cells, reducing the free cells in the box by two. We don’t yet know which way the candidates will be placed, but we do know that all both cells are needed for them, hence the exclusion.
The naked pair is one among many types of subsets. Naked subsets are pencil marked in box marking, because they restrict placement of other candidates, often leading to clues. Hidden subsets, another type of subset just as effective, normally wait for the second stage of basic solving, line marking.
Here’s a little sequence that suggests the action of box marking. Adding W3, a naked pair completes the 2 x 2 square that triggers the 1-slink in column 1.
In the blog, basic solving is documented by traces. Reading them is an excellent means of rapidly gaining experience.
Suppose you are reading a trace and have reached the grid below. The trace calls for NE8, and says that NE8 causes SW8.
Now you have to figure out why this happens. Why is NE8 where it is, and which cell in the SW box gets the 8. See why reading traces gets you on board the train? It’s your platform 9 ¾. Expect to have to picture several 8-slinks and use the positions of the other 8-clues to add that next 8. You can do it, and this shows how Sysdudoku techniques use human vision in an enjoyable way.
The puzzle is KrazyDad Super Tough v.5, b.1, #5, reviewed later. On KrazyDad.com, you get a treasure trove of puzzles at all levels.
Welcome to my blog. It’s going to be an eye opener, regardless of your current level of Sudoku.