Chains - Part 2 - Explaining Steps 1 - 11

Chains Part 2 - Explaining Steps 1 -11 - Finding Targets

SchuDoku Home      Chains - Part 1 - The 21 Steps   

My 21 steps for finding a chain in a Sudoku puzzle can be found here:  Chains - Part 1 - 21 steps

Here's my attempt to explain their use:


Consider the puzzle below, found in the PB Post, Jan 11, 2014:
   

Figure 0 - Original Puzzle with 55 empty boxes

The possibilities for empty boxes are all shown. Print it and try solving if you wish.
(To print, Right-mouse click, then select Print Image)


   Step 1. Be sure you've exhausted all other methods for teasing out solutions and eliminations

Applying "simple" methods should reduce the original puzzle to the following, which now has only 27 empty boxes:

Figure 1 - After "simple" methods are applied, 27 empty boxes. Be sure you eliminated as many possibilities (tiny numbers) as you can.

  2. Use an ink pen to circle the tiny numbers in all empty boxes that have only two possibilites - which I call "doubles:

Figure 2 - All Doubles now circled WITH INK.

To best follow along, I recommend that you now print either the puzzle just shown, Figure 2 , or - to practice circling doubles - print Figure 1 (the one with only 27 empty boxes) and circle the "doubles" yourself.  USE INK!!!!

»»3. Focus on one of the "doubles"

Figure 3 - One of the doubles has been boxed to focus on. You should NOT put a box around it. This was done to illustrate the instructions. "Which one should I choose?", you might ask. That is discussed later. I usually start near top, left.

4. Mark its "zone", i.e, its Group, Row, and Column.  (MARKING the zone is for learning purposes only. Normally, you would NEVER do this.)

Figure 4 - The "zone" has been marked.  The "zone" is all the boxes in the same row, column, and group as the "double" that we're focusing on. If you work with Sudoku puzzles, you mentally check out this type of zone ALL THE TIME!! 

 5. Focus on ONE of the numbers in the "double". I will call this number the "source". Do a quick glance to see if the source appears in any double OUTSIDE the zone.  If not, jump to step #20!

Figure 5 - Focus on ONE of the doubles inside the blue box. This becomes called the "source". I picked the "5". (Later I'll pick the 9) A quick glance reveals circled 5's in three doubles that are OUTSIDE the ZONE. Do not mark it yet.

 6. Briefly scan for a chain that can be a "way out" for the  source. If there is none, skip to step #20!

We've arrived at confusing techniques for finding chains.

Our "source" right now is the "5" that we chose.  We seek a chain from the blue box to a doubles box (OUTSIDE of the zone!) that also contains a "5".

In order to GET there, we begin with the "buddy," the other number in the blue box. In this case, it's a "9". 
There are at least two parts to this:

(Part 1) We seek another double IN THE ZONE that contains a 9, 
(Part 2) We look at ITS "buddy" and seek A LINKED DOUBLE, ANYWHERE that contains it, preferably OUT of the zone.
(Part 3! I said "at least two"!) If you're still inside the zone, then take the next buddy and try to find a linked double anywhere, preferably outside of the zone. Repeat until you're outside the zone or you quit trying.

"Huh?", you say.  It will be easier with the example. 

Before looking at the figures below, look back at figure 5. Do you see another double IN THE ZONE that contains a 9?

There's two of them. There's a 9/8 double at the bottom, and there's a 9/6 double at the right.

Figure 6 - Seeking a "way out" for the "source". The "source" is the "5" in the blue box. But the "way out" must begin with its "buddy", the "9". At least two "ways out" were found. 9/8...8/2  marked with green, and  9/6...6/9  marked purple. These marks are for learning purposes only.

It's worth spending time to understand the two chains that were initiated (neither was completed).

 Begin at B2.  Here's what's happening in my head as I seek them:

I'm focusing on 5, so I must start with the 9.

Scan the zone (group/row/column) and notice at the bottom:

9, 8  I whisper to myself. 

Scan doubles that are linked to B9, looking for an 8. 

On seeing G9 at the right, I murmur in my head 8, 2.

It's important to keep the order.  
       "9,  8", not  "8,  9".
       "8,  2", not  "2,  8".

Because a "way out" seems to exist, I will proceed to the next step.

  7. Make a faint mark on the source. 
Notice any "possible elimination". This is any tiny number INSIDE THE ZONE that is the same as the "source." They do NOT have to be found only in doubles.  
For learning purpose only, you should make faint marks on all the "possible eliminations". Soon, you won't bother marking them because it becomes annoying, and unnecessary.

Figure 7 - Our "source number" is 5. Note any other tiny 5's  inside the zone.  (They don't have to be in a double.) There are two of them. FOR LEARNING PURPOSES, one "5" has been marked pink, the other purple. You would not normally mark them.

  8. Scan OUTSIDE the zone for doubles that contain the source number.  These numbers are potential "targets"
Time saver: do not bother with doubles that were previously used as a source.
This is easy! It simply means that you are searching for any little CIRCLED 5 OUTSIDE of the zone. There are three of them. I'm first considering the one in I1 (top, right corner)

Figure 8 - All the circled "5s" OUTSIDE of the zone are "potential targets". In this figure, we are focusing on the "5" in the top, right.

9. For each potential target, decide if ...
    (a) it is linked to one of the "possible eliminations" (marked by learners in step #7) and if ...
    (b) on cursory examination - it might be an ending of a chain.  This is done by seeing if its "buddy" (the other number of the double) can be linked to ANY double ANYWHERE.
As always in Sudoku, two numbers are "linked" if they are in the same row, column, or 3x3 group.
CHAINS are extended when the "buddy" in a double can be linked to another double.

Looking at the "5" in I1, we want to see if it is linked to any "possible eliminations", i.e., any tiny "5" inside the zone.

Figure 9a - The "potential target", 5, in  I1  can be linked to two of the "possible eliminations" inside the zone. 

That satisfies condition  9(a)  for becoming a target.

For the second condition of Step 9, look at the buddy, the "3" inside that same top, right box. Then seek another linked double with a 3 ANYWHERE   Hopefully, you quickly find one.

Figure 9b - The potential target, the "5" in I1  has a "buddy", which is  "3".  Can the buddy be linked to ANY double ANYWHERE? Yes, as indicated with the green arrow. 

That satisfies condition  9(b) for being a target.

  10. IF the potential target meets both conditions of step 9, then faintly mark it. This number becomes a "target".

Figure 10 - The "5" in the top right has been faintly marked (gray).

You should faintly mark it on your paper.

11. Continue finding all targets. Targets are always OUTSIDE of the zone.

Figure 11 - Two targets were found for the 5. They are marked with gray. You should faintly mark them on your paper. Note that:

    * the targets are "doubles" that include 5 (our source)

    * the targets are OUTSIDE the "zone"

    * they link to a 5 INSIDE the zone

    *The 5 in box I6 is not marked to be a target because it does not link to a 5 inside the zone.

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Congratulations getting this far!
The next step is to actually look for chains from the source to each target.
There are two good reasons to hold off:
(1) There aren't any!!!  I already spent awhile looking.
(2) The first 11 steps involve most of the thinking and you need to practice them. That's what Part 3 is set up to do.

If you just want to get on with it, click for part 4.

 Back to SchuDoku Home
 Back to Part 1 - The 21 steps.
 Onward to Part 3 - Practice Steps 1-11, Finding Targets)
 Onward to Part 4 - Explaining Steps 12-21, Finding Chains