Twin Tagging

Twin Tagging

Some definitions:

• Twins — a House is said to have Twin 9s when there are only two Cells in that House which contain 9-candies (similarly for 8s, 7s,...).

• crown — To crown a candie in some Cell means to enter a Big Number equal to that candie in that Cell.

There are two different things that occur in a Grid which are important for basically the same reason:  a Pair, and Twins. Both of these possess a mutual-exclusivity quality that can give rise to the crowning of a candie:

• If a Cell contains a Pair and one member of that Pair gets killed, then the other member gets crowned. (The survivor becomes a Locked Single.)

• If two Cells in a House contain Twin 9-candies and one of those 9s gets killed, then the other 9 gets crowned in its Cell (same for 8s, 7s,...). (The surviving Twin becomes a Hidden Locked Single.)

Conceptually, these two ideas are very similar. But visually, they are very different:  a Pair is visually obvious, but Twins are buried and obscure.

Twin Tagging is a notational technique for making Twins visible and obvious on the Grid.

Which Tactics benefit from Twin Tagging?  These:

• Chains:  tagging a Tightly Linked Twin Chain.

• Smart Fork:  tagging Fault Points.

You resort to Chains or a Smart Fork only after you have carried out the less intricate Tactics but have still not reached a Solution. This means that you will apply Locked Sets, Claims, Fish, and URs before you reach the point where Twin Tagging might be advantageous.

In order to describe this notational technique, we need two more definitions:

• oblique — two Cells are oblique to each other if they do not lie in the same Row or in the same Column.

• aligned — two Cells are aligned if they do lie in the same Row or in the same Column.

To tag all the Twins in the Grid, do the following:

• If a Row has Twin 3s (say), tag them both with an underline:  3

• If a Column has Twin 4s (say), tag them both with a vertical bar:  4

• If a Block has obliquely located Twin 5s (say), tag them both with a dot:  O5

Remarks:

• The above ("3", "4", "5") are examples. In fact, you tag all the Twins in each Row, in each Column, and in each Block.

• Don't dot-tag Block-Twins that are in aligned (non-oblique) Cells, because this would add useless and misleading information. (Aligned Block Twins have already been tagged as Row or Column Twins: they're not a new set of Twins.)

• A candie with more than one Twin will be multiply tagged. For example, in the Cell {  2   5   O7  }, the 5-candie has a Row Twin and a Column Twin, and the 7-candie has three Twins, one in each of its Houses.

• (If your browser is Microsoft IE6, then click View / Refresh, because Microsoft randomly leaves off the underlines on the 5 and the 7 in the preceding paragraph, particularly when you use the upper or lower scroll buttons or the mouse scroll-wheel.)

Here's an example of a Grid that has been fully Twin-Tagged:

Twin-tagged Grid. All the Twins have been tagged. Look at any tagged digit in any Cell:  it's easy to find its Twins, and then to find the Twins of those Twins, . . . The two longest Twin Chains on this Grid are the 6-Chain and the 7-Chain (each of these has 6 Cells).  Find each of these Chains.

You will notice that, for reasons of legibility, I'm not able to use 3 x 3 candie layout (see Candie Markup) for the example Grids on this site. However, when you're creating and using Twin Tagging on paper, the 3 x 3 candie layout you use will make things much easier for you.

And there's another visual problem — as regards the dotting of oblique Block Twins, I haven't been able yet to find a way to produce, on the Grids on this site, a dot tag which is distinct & black and which doesn't louse up the Grid layout; so I have had to use a small circle.  But when you dot oblique Block Twins by hand, it should look like the 2 and the 6 in this Cell:

You will find that Twin Tagging done that way, along with the use of 3 x 3 candie layout, makes a Twin Chain in any particular candie very obvious on the printed Grid.

Before Twin Tagging a Grid, you will be in much better shape if you are using a Grid gotten from a site (see Links) that gives you a printout with all the candies printed initially in a 3 x 3 matrix in each empty Cell.  Alternatively, if you want to do Candie Markup by hand then enter the candies (in a 3 x 3 matrix) in ink, using a ballpoint pen. In either case, if you make a mistake while tagging Twins, you can erase the Tagging without erasing the candie.

The Twin-Tagging itself (underlines, vertical bars, dots) should be entered in pencil.

First, tag all the Row Twins. In each Row, do the 1s, 2s, 3s, then the 4s, 5s, 6s, and then the 7s, 8s, 9s. For each digit, don't look for only two (which is error prone), look for three of them: if there aren't three, then you've got Twins — underline them.

Then tag all the Column Twins. In each Column, do the 1s, 4s, 7s, then the 2s, 5s, 8s, and then the 3s, 6s, 9s. Put a vertical bar to the right of each Twin.

Then go back and check all the Row and Column Tagging. For a Twin-Tagged 5 (or 5), say "Only two 5s", and verify that. For a non-Twin 7, say "Lots of 7s", and verify that.

Then tag the Block Twins. In each Block, tag (with a preceding dot) all the obliquely located Block Twins. Consider the digit 3 (in a Block):  if you see any two 3s aligned in a Row or a Column, then forget the digit 3; otherwise, check if there are only two 3s, and if so, dot them. It's easy to see everything in a Block, so you're not likely to make mistakes.

OK, I know it's weird, my giving you such detailed advice. But you want to get so you can tag fast and reliably.

Twin-tagging a whole Grid takes me 10 minutes or less. At times, you will want to Twin-tag only a limited part of the Grid. The examples given on the Chain and Smart Fork pages will make it clear how much Twin-tagging you should do and why.