Sudoku Puzzle Sources — Printable Grid

These sites supply free Sudokus.  There's an option that will, on request, generate Candie Markup (pencil marks) in the empty Cells, and the print function will print the Candie Markup laid out in a 3 x 3 matrix in every empty Cell.

Sudoku Grid-from-Code Assistants

Many sites, particularly forums, make Sudoku Grids available in code form:

394  26.  8.1
.6.  13.  ..9
..7  9..  6.3

736  492  185
941  583  762
582  716  394

...  6..  237
62.  37.  .18
.73  82.  9.6

The digits are the original Clues, and the dots are the empty Cells.

A few sites have grid-from-code assistants; many of these will not accept code in the above format (with embedded spaces and newlines), but all of them will take code in linear form like this:


or this (with zeroes for the empty Cells):



Encyclopedic Collections of Tactics

Scanning Strategy

Bookkeeping Strategy

All the remaining links on this page are for the Bookkeeping Strategy, with its great variety of Tactics based on Candie Markup.

Hidden Locked Single

Locked Set

The term "Locked Set" is widely used for this concept (because it is consistent with the more recently developed concept of an "Almost Locked Set").  But a number of sites still use the older term "Naked Set", as you will see when you check out these sites.

Hidden Locked Set

Many sites omit the word "Locked".  (Cf. remark in preceding section.)



On all these sites, you will find the expression "x-wing", meaning 2-Fish.

Sashimi (of order 2)

You will find this Tactic referred to as a "sashimi x-wing".

Splatterfoot (of order 2)

All of these sites will refer to this Tactic as a "finned x-wing" or a "finned sashimi x-wing".

3-Fish & 4-Fish

A "swordfish" is a 3-Fish.
A "jellyfish" is a 4-Fish.

Frankenfish and Mutant Fish

Kraken Fish

Fishy Cycles

Fishnet Tactics

Both of the techniques listed below are conceptually enlightening and worth having a look at for that reason alone. But you may find that the labour involved limits their appeal.

Deadly Patterns

Unique Rectangle




The last three items are links to sites that discuss so-called nice loops:

A discontinuous nice loop is not a loop at all.  It's a Wrong Chain whose Driving Force consists only of Kills in Pair Cells and Surviving-Twin Crownings (no ALSes, no Almost Claims). When a Kill in a Pair Cell occurs, the lingo used is that this is the result of a "weak link". When a Surviving-Twin Crowning occurs, that is said to be the result of a "strong link".

Continuous nice loops look somewhat similar, but in fact they are substantially different.  Productive ones are rare, and I don't discuss these. You can read about them at these three sites.

Diabolical Sudokus — Current Examples

Diabolical Sudokus — Solving Techniques

This is the best site I can point you to for information on the powerful Tactics required for solving wildly difficult Sudokus:

The people at SudokuOne have developed a system called A General Logic for Sudoku, which is a coherent theory that unifies the reasoning behind all Tactics. It includes a concrete graphic method for indicating and applying (even very complex) Tactics on the Grid. The site has links to explanations of the method.

In addition, SudokuOne offers a free downloadable program called Xsudo which is designed to help the user learn the logic by working with real Sudoku Grids. Any Grid can be input. If you want, you can activate a gradual solver that gives diagrammatic and verbal feedback on the successive moves.

Xsudo is capable of solving Diabolical Sudokus. Whether a human solver could really learn to use the most complex Tactics available in A General Logic is possibly a matter of argument. But the system is extremely impressive.

Almost Locked Sets Technique

Long-winded remarks before the list of links —

The components of a Wrong Chain or a Gotcha Chain are just Pair Cells for the most part, but an Almost Locked Set (ALS) can occur as a component, and this addition greatly extends the power of Chains.

Beyond that, people have developed a technique based on the use of several Almost Locked Sets which are linked together by candies referred to as restricted common digits. In principle, if you can find ALSes on the Grid that are correctly linked by restricted common digits, then you can achieve a Kill without actually having to trapse through a Chain.

But in fact, if you look at examples of the ALS technique and you just forget about the ALSes, you'll find that if you make use of the Cells indicated in the example, you can construct a Gotcha Chain or Wrong Chain to achieve the desired Kill. For most of the examples you'll find on the web, the equivalent Chain will consist of only Pair Cells plus possibly an embedded ALS. It is possible to run across a rather difficult example where the Chain emulation will require that the Chain contain an embedded Almost Claim (and you will recall that this is not an easy construct to see).

A characteristic of the ALS technique is that it is aimless (not directed): you look for the ALS pattern without regard to what it might kill, and you then look to see whether it actually has a victim. A corollary of that fact is that if you were trying to achieve the same thing with Chains that people accomplish with the ALS technique, you would in fact try to construct any two-headed Gotcha Chain on the Grid, without a specific target in mind. Or you would try to construct a Wrong Chain from some utterly arbitrary candie.  But in fact none of this is easy, since you would normally use the ALS technique, or else an aimless Gotcha Chain or a random-victim Wrong Chain, only on an extremely difficult Grid where you have run out of good Tactics and would settle for killing any single candie whatsoever.

The ALS-technique terminology is problematic (from my point of view). In the treatment of Chains on this site, I have referred to the two Cells {26} {268} as almost a Locked Pair, because if the 8 were killed, the two Cells would become a 2,6 Locked Pair (which is what happens when you traverse the Chain.)  But ALS-Tactic terminology calls {26} {268} an almost locked trio, on the grounds that it is "missing" a needed third Cell containing only the digits 2 and/or 6 and/or 8. Since nothing in the ALS-technique reasoning suggests that these two Cells could actually become part of a Locked Trio on the Grid, the terminology seems strange, and that probably contributes to the lack of interest in this technique on the part of middle-of-the-road Sudoku players.  (However, I've noticed that in more recent writings on the ALS-technique, people have avoided the confusion above by simply referring to any of the components involved as an almost locked set, avoiding any description of it as a pair or trio or whatever. That's good.

I don't cover the ALS technique on this site, and I have no plans to do so. If I applied every Tactic I know and still had an unsolved Grid, I would probably declare it diabolical and go have a beer. If I were feeling masochistic, I might do as I indicated above and scour the Grid trying to construct an aimless Gotcha Chain (one that kills something somewhere), or I might try to construct a Wrong Chain from some arbitrary candie if assuming it true created a new Locked Set that would give me some moves to start a Chain with. I might even look for a Chain with an embedded Almost Claim. For awhile. But that's my limit.

Nevertheless, you may want to have a look at these links to material on the ALS technique to decide for yourself what you think. (Optionally, for any example you look at, you could see if you can construct a Gotcha Chain or a Wrong Chain to achieve the same Kill.) These sites are the ones I've found so far that do the best job of explaining the almost locked sets technique:



This page was last updated on 2011 January 7.

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