External synonym: pencil marks.
A Sudoku Grid is a puzzle that is defined by the original BigNums (Big Numbers) given in some of its Cells. And of course you may have added other BigNums via the process of Scanning.
If the Sudoku isn't easy, then you will reach the point where you have done as much as possible by Scanning, but there are still empty Cells left on the Grid (usually a lot of them).
Sudoku players learned early on that if you're willing to enter in every empty Cell a complete list of all the digits which that Cell might hold, then it becomes possible to apply a variety of powerful Tactics to complete the puzzle.
Each of these possible digits written in an empty Cell is called a candie (or a candidate). The candies in an empty cell are written small, of course. We'll look at that in a minute.
Collectively, the possibility list of candies in every empty Cell is referred to on this site as Candie Markup. On other sites, you will instead find the term pencil marks used for this concept. Since you will find it more advantageous to enter Candie Markup in ink, I will not use the term pencil marks.
The ensemble of new Tactics that are made possible by Candie Markup constitutes the Strategy of Bookkeeping, so named (on this site) because it involves the placing and updating of the acceptable list of candies in every empty Cell.
Before we can get down to business, we need to define this term:
Since no House can contain duplicate BigNums for any digit, a Cell's Buddies are important: a Cell cannot possibly hold a value that already exists as a BigNum in one of its Buddies.
Now for the details. When you enter the candies in an empty Cell, you write them in small, in ink, in the following 3 x 3 pattern:
Of course, any given empty Cell will allow only certain candies, so an actual candie-marked Cell might look like this:
This means that this Cell has restrictions on it imposed by its neighbours (its Buddies) which will allow it to hold only a 2, 4, 6, or 7, nothing else. Why is that? Because this Cell's Buddies already contain, collectively, the candies 1, 3, 5, 8, and 9, which leaves only the possibilities 2, 4, 6, and 7 for the Cell we're focussing on.
Why enter the candies in ink? Well, you may only rarely want to erase a mistake you've made, but when you do, you'll be very glad that the erasure doesn't obliterate the Candie Markup. For all the subsequent work (crossing out candies and entering a BigNum in a Cell), you'll use a thick-lead pencil, and the inked Candie Markup really won't get in the way.
So each candie in a Cell is a possible value of the BigNum that will finally be placed in that Cell. And where does the list of candies in a Cell come from? Simple — as we already indicated, it's the list of all digits excluding the BigNums in the Cell's Row, the Cell's Column, and the Cell's Block. In other words, it's the list of all digits not equal to any BigNum that occurs in the Cell's Buddies.
Writing in every empty Cell's candies by hand will take you awhile, possibly 20 minutes. You'll develop your own ways of doing this efficiently. (For example, I candie-mark the empty Cells of the fullest Houses first — try doing it that way.)
So why take up so much room in the Cell with the little 3 x 3 matrix holding the candies? Because this convention makes it easy to see all the Cells in a House that hold a 9-candie, or all the Cells in a House that hold only a subset of the set 2,5,8, or the one single Cell in a House that will actually accept a 4, or the fact that there are exactly two Cells in a House that hold a 7. Specifically —
It makes the patterns you will be looking for (Hidden Locked Single, Locked Pair/Trio/Quartet, 2-Fish) much easier to see.
It leaves enough room to add the symbols required for Twin Tagging.
There are web sites that will let you download and print large-size Sudokus with the 3 x 3 Candie Markup (pencil marks) already done for you; two such sites are listed on the Links page. I strongly recommend that you go to one of these sites, print out three Sudokus of medium difficulty, and then apply some of the Local Tactics (see the menu above). I recommend that you try this for two reasons:
You might very well prefer to always work Sudokus that have the Candie Markup (pencil marks) already done for you, since putting them in is an utterly brainless task.
Even if you generally insist on putting in the Candie Markup yourself, working a few pre-marked Sudokus should convince you of the advantage of using the 3 x 3 candie matrix (in case you have any doubts about that).
If you decide to make use of one of the two sites that will give you 3 x 3 Candie Markup pre-done, you have two different ways of proceeding:
Ask the system to supply (or "update") the Candie Markup (pencil marks), print out the Grid, then forget about the Scanning Strategy and just jump immediately to the Tactics that fall under the Bookkeeping Strategy (see the Strategies page).
Or, since the system will let you do Scanning online, do that to fill in as many empty Cells as you can. Then ask the system to write in the updated Candie Markup (pencil marks), print, and apply the Bookkeeping-Strategy Tactics to the printed Grid.
It may seem daunting that, every time you apply a Tactic that results in the entry of a new BigNum in some Cell, you will have to update the Candie Markup in the Grid — but in fact it turns out to be easy.
This is all it amounts to: any time that you execute some Tactic that causes a 9-candie in some Cell to be crowned (entered as a BigNum 9 in that Cell), you have to kill (cross out) the 9-candies in all that Cell's Buddies. (The Buddies of a Cell are all the other Cells in its Row, its Column, and its Block.) The same remark applies to a newly crowned 8-candie, 7-candie, . . .
This is what a Cell looks like when two of its original candies have been killed:
The reason that this process of updating the Candie Markup is fast and easy is that you have placed all the candies in their assigned place in the 3 x 3 matrix in the Cell. When you want to kill all the 6s in a group of Cells, you know exactly where a 6 will occur in the matrix of each Cell.
Before you try it, you might think that spreading the candies out like this won't leave room for the final BigNum you enter in the Cell, but at that point you're using a thick-lead pencil, and it's easy to make the BigNum entry quite clear.
The resolution of a "high" definition video monitor is about one-tenth the resolution of a printed magazine page.
The unfortunate result of this is that if I used digits small enough to fit into a 3 x 3 matrix in the Cells of my example Grids, they would be illegible. So you will have to tolerate the less than optimal candie layout. At least it's possible to read it.
Neither you nor I will live long enough to see high definition video.
This page was last updated on 2010 November 28.
The home page for this site is alcor.concordia.ca/~stk/sudoku/