This post reviews the Chapter 9 of Peter Gordon’s Sudoku Guide, entitled Forcing Chains and Grid Coloring. The guidance is very limited, and what there is, promotes guessing as opposed to solving by logic.
This verdict is confirmed in the first topic of the chapter, the XY wing. Going back to the Sysudoku schematic of the wing, picturing the wing and a victim candidate, I described it as a bv chain connected by weak links, in which a toxic set is generated. If either of the wing’s Z candidates is false, then the other wing’s Z has to be true. Since one of them is true, the Z candidate that “sees” them both is false.
Peter leaves the structure of the wing unspecified, but places it on the grid where the soft links are evident. When you try both X and Y values of the hinge, either value makes the outside Z false.
These descriptions may seem equivalent, but they are not. The sysudokie version expands easily into longer XY chains with matching end candidates, and into forms with weak links other than shared units. The Gordon guide version makes it to be a form of trial and error, which is fictitious, because if you recognize the structure, the result is always the same.
The Guide explains very few solving structures, but does explain the XYZ-wing. To do so, Peter introduces his concept of the “seeing”. A cell sees its buddies, which are its fellow occupants of its row, column and box. On that side of the pond, cells, not candidates, see each other.
The XYZ-wing is defined this way: “Any cell that is buddies to all three of the XYZ, XZ, and YZ cells cannot contain a Z.” Accurate enough, but what is he talking about? A toxic set of three Z candidates. It’s the outside Z that is the victim, not the cell containing it.
But why is a toxic set generated? Peter falls back on his forcing chain version: Whether the hinge cell is X, Y, or Z, the victim Z will be forced to false. We’d explain it that regardless of the hinge value one of the wing’s Z candidates has to be true.
Guide readers are to try X, Y , and Z and see what happens. Sysudokies are looking for possible “seeing” chains that tie together irregular wings or allow potential victims to see the toxic sets.
As to longer chains, here is the Gordon Guide’s advice:
“Sometimes you can find situations more complex than XY-wing or XYZ-wing where there are two possibilities, either of which leads to the same result. Here’s an example:”
An example of what? XY chains, and all other AIC are left out. Some guide.
So where do “Forcing Chains” of the chapter title come in? Peter seems to think that the act of trying multiple candidates of a cell to see what happens is a forcing chain. That would certainly be something experts don’t know about.
In the next section, Grid Coloring, Peter adds some helpful technology to picking a value to see what happens. Early on, I called this a truth net, and warned beginners of its nihilistic consequences. Grid coloring has nothing to do with Medusa coloring , the representation of slink nets intensely exploited by sysudokies. That “coloring” is addressed haphazardly in the next Guide chapter. Besides, Peter only applies Grid coloring to one value at a time, i.e. to X chains. Grid coloring is a little like the trials we use on very hard puzzles, except that it’s a single arbitrary value on trial, not a logically constructed set of values.
Can I mention, in connection with the bv scan, two more glaring omissions in this Guide? One is the Sue de Coq, a very effective elimination method. Even the verification of its structure solves puzzles. The second glaring omission is any real help for finding all possible wings, or chains of any type.
The title the final section in this chapter is Turbot Fish. You might be thinking that Peter will be talking about X-chains and loops. But no, it’s about his truth net, the grid coloring technique. Peter just wants to show us how grid coloring discovers a turbot fish. Ironically, the Guide is not published in color.
“It requires five cells that are arranged so that two pairs of cells are in the same rows, two pairs are in the same columns, and two cells are in the same box. If three or four of the pairs are the only places where a particular number can go, you have a turbo fish. If there are only two such pairs, then it still works, as long as those two pairs don’t share a cell. “
OK, got it? Start grid coloring. What’s that? Oh, Peter didn’t mention it, but we are looking for an X-loop. That’s how five cells can have pairs of the same number in two rows, two columns and a box.
A pair of the only two places a number can go is a slink. Now sketch this out. Got a piece of paper? If three of the loop links are slinks, you have either an eliminating almost nice loop(ANL), with the two winks together, or a confirming ANL, with the two winks apart. If only two are slinks, then the slinks must have a wink between them, and the two intersecting winks eliminate the intersection candidate. The four slink case is an eliminating ANL, with the two slinks apart from the wink used as winks.
So we have solved Gordon’s riddle and know what to look for. But now can you tell me why you would do that by picking a candidate to be true and following it around the grid to see what happens? That’s finding a turbot fish by grid coloring.
If you sketch in the slinks and fill in the winks, they jump out at you. Sysudokies don’t search for Turbo Fish or any other special type of X-chain. They construct X-chains and watch them form loops, and toxic pairs. The X-panel helps you focus on that. From the 9-panel, a simple 9-chain ANL removes 9r4c5.
The Gordon Guide doesn’t cover X-chains, but has room for a laborious search for the very specialized, rarely encountered turbo fish. A perfect way to discourage new solvers. Don’t give it to a friend, without telling her about these review posts.
We’ll finish up our Guide review next time by reporting how Gordon overspecializes and fails to explain, alternate inference chains. AIC’s are a matter of some importance in advanced solving. Maybe you’d like to do the basic solving on his Example 32, which illustrates what he has named the Nonrepetitive Bilocation Cycle. We’ll checkpoint that, and tell you what it really is, next time.