## Sysudoku Basic Subsets in a Sunday 5-Star

In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins .

In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins .

In this post, a Dave Green Sunday 5-star illustrates how naked and hidden subsets are spotted in Sysudoku Basic, a 3-stage process to identify candidates, and solve many Sudoku puzzles in the process.    Sysudoku Basic finds clues and subsets while accumulating candidates. Many solvers and most Sudoku literature use the keypad style of representing candidates, and a mechanical process that generates all of the candidates permitted by the given clues before any solving begins.

The purpose of Sysudoku Basic is to identify clues, subsets and strong links (slinks) and all candidates consistent with them, without generating many candidates that are eliminated before they contribute to solving.

A strong link is a pair of candidates, which includes at least one true candidate. The first stage of Sysudoku Basic is the Bypass, so called because it records on the grid along with clues, only the candidates of subsets. Strong links are recorded in a two further stages, box marking and line marking.

Here is the general definition of a subset:

How can a set of n values in a set of n cells be known to be the solution values? In a naked subset, there are no other values in these n cells. A single candidate of each value must eventually be placed in each cell. Candidates of these values in the line or box outside the subset are removed.

In the hidden subset n values in a box or line are found to be confined to n cells. Each of these cells will eventually claim one of these values, so candidates of other values can be removed from the confining cells.

As to singles, a naked single is a cell with a single value in it.  A hidden single is the only cell in the house with the value in it. The keypad number scanned grid is great for spotting singles. But in Sysudoku Basic, we get a lot farther, while looking for clues, not singles.   Let’s just do the bypass and see how the subsets show up.

Here is the grid after the bypass. Two 4-fills occurred and one was resolved. In the bypass, we’re into clue patterns, not candidate patterns.   Of the 10 clues found, there was one naked single and five hidden singles.

In the keypad grid, see if you can use the candidates to find the naked single and hidden singles. In the bypass, we don’t look for them. It’s not the right time.

As it happens, an advanced technique does begin here, showing how the uncluttered basic grid supports more than basic. As you mark the r6 4-fill, you might notice that C5 and SW5 leave only the same two columns for 5 in r1. That establishes a 5-wing in r1 and r6.

In the bypass trace, we put the 5-fill on the top line. It’s there to account for the 5-wing. Note how a subset pair (a subset with n =2) is marked in the trace.

The red symbols mark the  5-wing in r1 and r6. The wing will remove 5 candidates in c3 and c8, as the rows are marked.  In the bypass and box marking, how are box, row and column slink partner candidates distinguished?

The box marking trace lists the boxes containing a slink for each value. A box slink is exactly two candidates of a value in a box, a strong link. The list includes aligned triples, marked by “t” after the box name. Slinks are listed as effects, when they are caused by another slink.

A hidden pair 56 occurs in r1 above, when 6 is limited, along with 5, to the same two cells in r1. It’s a “hidden” pair because these two cells are reserved for 5 and 6. When r1 is marked, any other candidates, like the number scanned 1, 3 and 7 candidates on the keypad grid above, will be removed.

In line marking, the lines with fewer unfilled cells go first. Filling a line can effect other lines, changing the order. The list starts with 3 and 4 fills, then comes  r1, and a naked triple.

After the ouside 1,3,7 candidates, of the hidden pair 56 are removed,  the naked triple subset becomes obvious. As other rows are marked, no 5 candidates will be added to c3 and c8.

As lines and boxes are covered in line marking, ‘look for subsets as we begin to see all candidates in each line and box. We watch the values smaller in number. Naked subsets are the more obvious.

When we get to r2, the first 6-fill, you probably saw the naked triple 137 as soon as the line was filled. But a hidden is there as well. Let’s consider how to find them, based on this example.

For naked subsets, look for cells containing the same values. For hidden subsets, look for values limited to fewer cells. Here’s a definition designed for finding them.

The keyword is “confined”. We found the r1 hidden pair when we knew 5’s were confined to columns 3 and 8, and we realized that 6 in r1 was confined to the same 2 cells. In r2, we see the two values 2 and 4 in only two cells for a  hidden pair.

There is another hidden triple in r2, but the hidden pair 24 in r23 and r25 eliminates additional candidate 5r23 for the clue NE5, which destroys the 5-wing, but adds two more 5-clues. .We picture subsets by curves surrounding the candidates and diamonds around eliminations.

The collapse :

This post concludes the series of Dave Green Conceptis puzzles illustrating techniques in recent Sysudoku Basic.

We’ll follow with a few basic level puzzles from a new series replacing the Dave Green Conceptis puzzles in my newspaper, the Akron Beacon Journal.

But first, next post is an updated basic solving of Royle 17-13727 earlier posted 11/15/2016. You can look that post up by date by the monthly archive list on the right. The post next week features its 4-fill resolutions and its box hidden triple, and illustrates looking up a puzzle by subject tag.

As to 4-fills, I went back to the KrazyDad Insane review of a very tough collection which was updated before I used 4-fills extensively, to see if 4-fills would make a decisive difference. There was not one resolvable 4-fill in the review.

If you want to look up a collection review in on the monthly archives list, go to the Titles page and slide right onto the collections titles for post titles with monthly archive dates. Try it out. You might be surprised.