Here’s the basic trace on the Saturday Dave Green 4-star shown at the end of last week’s post. It survived the three Sysudoku Basic phases: bypass, box marking and line marking. It’s the first I remember.

Let’s talk through the Sysudoku marking of the bypass. It’s short enough to bring up every attention point, but it’s best to read it as you mark your own grid.

In the 1 scan, the NW crosshatch has 3 cells for 1, the E dublex 2, and the S dublex 2. We’ll mark the box slinks in box marking. The 2 scan will create slinks in 4 boxes. Then for 3, a crosshatch into SW creates a slink and dublex to complete a wall with NW3 and a 4-fill in c3. We follow the slinks in NE and E, and return to scout the new NW wall. What new dublex will it create? The value 7 is not in the wall, and the limited crosshatch produces NW7.

The 1 crosshatch into NW now leaves one cell for NW1. Now there’s a NW 3-fill, missing 5, 6 and 9. No sweepers, so we continue the 3 scan with cross hatches into E and SW. Slinks are bypassed for 4 and 5. The single 6 can take no action.

In the 7 scan, first a slink in W, and then clue C7 generating a double crosshatch for W7. Now looking in the other direction, a new 4-fill in c5. As we go, more and more 3 and 4-fills occur. Look to see if values in the side lines are missing in other boxes. Values 1 and 7 are not missing. The N6m slink is noted.

On every new clue, an automatic check for a 3-fill. W7 yields c3[689]. The rule is two hits on a cell or two values on two cells. When a line 3-fill is not immediate, we post a fill string reminder. Continuing the 7 scan, the last box is double crosshatched for SE7, Two 8 crosshatches for nought. On the 9 value, the NE crosshatch dublexes SE9, which supplies that second 9 seeing the 3-fill cells. We put the effects list in brackets to say it resolves a 3-fill.

Box marking is a routine posting of the slinks we saw in the bypass, until we get to the SE box on the 6: list. As the 6 slink is added, my count verifies the match of cells and values. With no more additions possible, 5r8c9 is obviously true. But the more direct analysis seizes on the new hidden pair 16, and two accompanying clues.

The effects of that list is extensive, but somehow the 4-star survives. Maybe there’s a side effect overlooked along the way. Read it out on your grid and if so, let me know.

Another possibility is a slip up in line marking. Here’s my line marked grid after the close. Did I miss a subset?

Now from here, you can enter advanced in several ways.

My choice is unique rectangles, because a readily spotted pattern can be looked up in a table for corresponding eliminations. Here we have a type 3 where the extra contents of the ceiling corners forms a hidden pair eliminating 8r6c9, and a type 1 where either 6r1c9 or 6r7c8 eliminates 6r1c8 to create a double solution rectangle that Dave Green would certainly not publish. The collapse from (E6, E8, NE1, SE1) is immediate.

Now advanced readers have waited long enough. The review of Stefan Heine’s *Sudoku ultrahardcore 1* begins next post, with the ultra 3 shown in the previous post.

In his book of 500 puzzles, Stefan informs us, puzzles on the left page can only be solved with the most complicated methods. But no one will find a logical way through even one of the 250 on the right. To me, this sounds like a perfect setting in which to explore the quite logical Sysudoku concept of *trials*, so I’ve committed to 10 from the collection of upper right page puzzles.

In his subtitle “Intuition schlagt Logik”, what does Stefan mean by “intuition”? The term lacks the objectivity of “logic”. In Sysudoku, “intuition” is not taken to mean “trial and error”, the repeated trials of largely arbitrary choices, confirmed only by the contradictions reached by alternatives. This technique does, in time, solve the most difficult of puzzles, but without insight into any puzzle’s logic.

Instead, we’ll take “intuition” of ordinary meaning to have a role in what has been identified as *trials*, and seldom invoked, in the blog. A trial is two mutually exclusive partial solutions, one of which must be true and the other false. In a trial, intuition guides the decisions that our methods are not enough, and how we will construct a trial. Experience refines our intuition as to when a trial is going to be decisive. We want enough evidence on both sides, for the contradiction of the wrong choice to come soon, and the right choice to go all the way.

Sysudoku employs a different trace method for trials. The normal trace is depth first, the squirrel going as far out as possible before turning back to a branching limb. A trial trace is breath first, an army of squirrels advancing out in inference lock step, until a contradiction is reached. Breadth first tracing provides a measure of just how obvious the contradiction is. Also in trial tracing, when we get a solution but suspect there may be more, we try the alternative. There are several instances o occurring here.

After the coming long review, you’ll have 240 more ultrahardcore right page Ratsel to refine your intuition. We’re not saying that a solution by trial is as good as a logical solution without trial. On the other hand, when right page ultrahardcores fall by Sysudoku trial, we don’t expect to hear that logic has been somehow defeated.