A Strategy is a collection of Tactics. Any Strategy has a concrete overall approach that determines what Tactics are actually possible. A simple Strategy's approach can be limiting, in the sense that it may allow only a small set of Tactics.
A Tactic is a specific kind of move (or set of moves) that will change the status of the Grid in such a way as to bring you closer to a Solution. Since a Sudoku looks like such a simple puzzle, it's amazing the number of Tactics that people have invented (because Sudokus turned out not to be so simple after all).
There are two known Sudoku Strategies: Scanning and Bookkeeping.
Through a cooperative effort on the Internet over the last several years, the Sudoku community has developed, exemplified, and explained various Tactics that fall under these two Strategies.
The menu at the top of every page gives you access to explanations of the particular Tactics that are presented on this site.
The remarks below give an indication of the order you might follow in applying the Tactics of a given Strategy. However, these are only suggestions — I take it for granted that you will, in fact, develop your own way of doing Sudokus.
In pure Scanning, you look at the currently existing Big Numbers entered on the Grid and apply logical Tactics that prove that some particular Big Number must be the one that has to be entered in some empty Cell.
(Specifically, for Scanning, you do not maintain an updated list in every empty Cell of all the digits the Cell might accept.)
The Scanning Strategy is very enjoyable, and it is often sufficient for solving easy Sudokus. (For hard Sudokus, you can use Scanning to fill in some of the empty Cells before you switch to the Bookkeeping Strategy.)
Scanning Tactics —
You always have to keep your eye out for a Nearly Full House and then apply that Tactic immediately.
Row/Column-on-Block Shadowing is easy (and fun). Apply it again and again for as long as you can.
When you're stuck, switch to the other two forms of Shadowing. Once these have paid off once or twice, most people see if they can switch back to Row/Column-on-Block Shadowing.
When you can't get any further with Shadowing (and you've checked for the existence of a Nearly Full House), then you have a choice:
forget Scanning, and switch to the Bookkeeping Strategy;
or stay with Scanning and try the Only Digit Tactic (which is slow).
If you go the second route and Only Digit pays off for some Cell, you might be able to switch back to Shadowing.
If you reach the point where none of the Scanning Tactics work, you again have a choice:
put the Sudoku in a shredder;
or switch to the Bookkeeping Strategy.
For Bookkeeping, you use Candie Markup (pencil marks). This means that you first create a list in every empty Cell of all the candies it could accept, and then, subsequently, you modify these lists every time you apply a Tactic, and you update the lists every time you enter a new Big Number in some empty Cell.
Creating the Candie Markup in every Cell is hard; modifying and updating it is not hard at all.
For creating the Candie Markup you have two choices:
after Scanning, ink in the possible candies in a 3 x 3 matrix in every empty Cell as indicated in Candie Markup;
or just print out the original puzzle with the Candie Markup already done for you by a web site that offers this service (see Links).
I urge you to try the second method for a total of three medium Sudokus; if, after working those, you don't like that approach, then I can't argue with you. For me, obviously, I begrudge the 20 minutes it costs me to carry out the mindless task of initially entering the Candie Markup when there's a machine volunteering to do it for me.
People have developed so many Bookkeeping Tactics that they fall into several groups —
Local Tactics —
Grid-Sweep Tactics —
Uniqueness Tactics —
Network Tactics —
These groups are listed in (chronological) order of application, but this is by no means an ironclad rule. You can't louse up a Sudoku by applying Tactics in the "wrong" order, because every Tactic is a logically correct procedure.
You have to keep your eye out at all times for a Locked Single (which is gloriously obvious) and a Hidden Locked Single (which is not), and then apply the corresponding Tactic immediately. These are the most important moves you make, since they fill an empty Cell.
Virtually everyone applies the Local Tactics first; together these are referred to as "the basic logic". But do you do Locked Sets first, or Claims?
Rule of thumb —
When the candies in the empty Cells are not dense (meaning there are a reasonable number of Pair Cells and not very many Cells containing four or more candies), then do Locked Sets first.
When the candies in the empty Cells are dense (meaning there are not very many Pair Cells and a lot of Cells containing four or more candies), then do Claims first.
Is that rule a little vague? Yes, it is. But candie density is still a good criterion for the choice, and you'll develop your own feel for it.
Incidentally, when you've gotten very fluent at all this, you'll probably start out by just eyeing the Grid and applying all the easy stuff you notice — the Hidden Locked Singles, the Locked Pairs, the Locked Trios, because they're all so easy to see. And then after that, you'll apply Locked Sets and Claims methodically, checking every Block, Row, and Column.
It's worth remarking that when you're doing Locked Sets and Claims, an odd phenomenon can occur. Sometimes you'll notice that you've just crowned two 9s in quick succession. When that happens, you may be having an epidemic of 9s: so temporarily interrupt what you're doing, and check every Block to see whether it has a 9-candie Hidden Locked Single (about one-third of the time, you will be rewarded with a bunch of them). In principle, you should have to check the Rows & Columns, but, oddly, it seems to suffice to just check the Blocks. (All this obviously applies to 8s, 7s, 6s,... too.)
After the basic logic you'll do Grid-Sweep Tactics, looking for 2-Fish. This is slow when you're just starting out, but you'll get faster. And when you do get proficient at 2-Fish, you'll incorporate Sashimis and Splatterfoots (see 2-Fish) in the search process. The Fish don't produce prolific kills, but you can't do without them.
And then you'll look for Unique Rectangles (URs); these are very
easy to find. If you run across a 1-corner UR, you've just been given
a gift, and you'll apply it immediately. If it's a 2- or
If at any point you have eliminated so many candies that the Grid now consists of only Pair Cells except for one or a very small number of non-Pair Cells, then you may (or may not) have arrived at a BUG+n. If it's a BUG+1, it will be clear, and that's a gift too — apply the Tactic for that, and you'll have a Solution. If it's a BUG+2 or a BUG+3 (which has to be carefully verified), then you'll be looking for Consensus Chains or Troublemaker Chains, which you very often will be able to find. Examples are given on the BUG+n page.
Of course, if you see an obvious 2-Fish or an easy UR at any point whatsoever, you can apply it immediately.
After all that, it's possible that you still don't have a Solution. You might want to look the Grid over for any Local Tactics you missed, especially Hidden Locked Singles and anything that you have a tendency to miss (I overlook a Claim sometimes). If you're really stuck, then it's a hard Sudoku, and you'll want to haul out the big guns: Chains.
A Chain is a very satisfying way to finish off a hard Sudoku. You're no longer looking for a set pattern — you have to create your own pattern to attack and demolish a Worthy Target that you have located on the Grid. The creative logical thinking used in constructing a Chain will leave you with that wonderful feeling that you've solved the Dragon's riddle.
And what if you can't find a Chain? Maybe you still want the
satisfaction of arriving at a Solution; if so, you'll check the Grid to see
if a Smart Fork is possible.
This Tactic is based on
the logical determination of a Fault Point through the process of
Twin Tagging. If a
This page was last updated on 2011 January 7.
The home page for this site is alcor.concordia.ca/~stk/sudoku/