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Lesson #6B. Check for BLOCK OUTS (cont’d)
Our third example introduces a new concept: RESERVED cells.
In the Sudoku puzzle fragment below, look at the possible Cells where the number 9 can be placed in the UPPER LEFT (7-8-6-4-5) and UPPER CENTER (6-3-2) blocks.
Marking up the grid with the obvious BLOCK OUTS yields:
Let’s label the available cells A, B, C, and D.
Each of the Blocks offers two cells where we could place a 9. For the UPPER LEFT Block, both A and B are in the Column 3. For the UPPER CENTER Block, C and D are both in Row 3. Since these are the only Cells where a 9 can go in these Blocks, we can say that the UPPER LEFT Block has RESERVED Column 3 for the number 9 and that the UPPER CENTER Block has RESERVED Row 3 for the number 9.
I’m using the term RESERVED in the same way that you’d use it if you reserved some seats for an event. You and a friend have tickets, you know the location of them (row and seat numbers) but who’ll sit where hasn’t been determined yet. You’ll figure that out one you get to the event and see who’s sitting next to you on either side, if there’s a tall person in front of you blocking the view from one seat, an aisle or empty seat next to one of you, etc. You need the additional information of being at the venue and taking into account the impact of the surrounding attendees in order to figure out exactly where everyone will sit. But, even so, you know that the two seats are RESERVED for you and you’ll definitely sit in one of them. The same kind of thinking applies to this use of BLOCK OUTS. We know a 9 will be placed in either A or B for the UPPER LEFT Block and in either C or D for the UPPER CENTER Block but we can’t specify the exact cell just yet.
So is that all we can do at this point?
No, we’ve got one more logic trick up our sleeve. Since B, C, and D are all in the same Row, we can deduce one more piece of very useful information. If we hypothetically place a 9 in either C or D (and in fact, we will eventually have to do just that as 9 can only be placed in C or D for that Block), then there’s no way that a 9 can ever be placed in B also. So if we update our diagram with this additional BLOCK OUT information, it now looks like this:
Thus, we’ve eliminated B as a location for the number 9 in the UPPER LEFT Block and therefore, location A must contain a 9 as it is the only unblocked cell for that number.
We still haven’t solved whether C or D will contain the 9 so we’ll have to leave that as an unsolved placement at this time but we have been able to use BLOCK OUTS in a more sophisticated fashion thus adding another arrow to your Sudoku logic skills quiver.
Our final example of BLOCK OUTS also uses a combination of techniques.
Take a look at this next Sudoku puzzle segment and focus on the occurrences of the number 6.
At first glance, it doesn’t look like you can draw any conclusions. But take a closer look. In the UPPER LEFT Block (2-5-3-4), and notice that the top row is filled. In the UPPER CENTER Block (1-6), there’s a 6 in the bottom row of the Block thereby eliminating any other 6’s in that Block. In the UPPER RIGHT Block (1-5-4-2-3), there aren’t any 6s and there are two empty cells in the top row (just to the right of the 1.) So using just the information from the Row Block 1, we can’t place an additional 6.
But look at the RIGHT MIDDLE Block (3-4-6). It does have a 6 that blocks Column 9. Let’s put all of this information together by drawing the BLOCK OUTS that we now have and seeing where that leaves us.
Well now, that’s much more revealing. We can obviously place a 6 in the Cell at Row 1, Column 8 (just above the number 5.).
This example showed how you can use a combination of Block Out techniques to see if an instant number placement is possible. The bottom line: Leverage the Sudoku numbers that are already in the puzzle grid by using a variety of BLOCK OUT techniques and you’ll find it so much easier to quickly and correctly place numbers
Quick Reminder Checklist for BLOCK OUTS:
- Look for any number that appears twice in any ROW or COLUMN BLOCK - Mentally block out the associated Rows and / or Columns containing those numbers. Can you place the number now? - If not, check for the existence anywhere in any of the associated Blocks (remember that once a number is in a Block, it can’t appear again in that Block regardless of the Row or Column it’s in.) Can you place the number now? - If you still can’t place a number, check for any other occurrences of that number anywhere else in the Sudoku puzzle grid that might BLOCK OUT an associated Row, Column, or Block. - If you still can’t place the number, check to see if and Rows or Columns have Cells that have been RESERVED for the number and if the Row / Column intersects with and eliminates one or more of the available Cells for the number in question. - If you still can’t place the number, move on to another cell and try to resolve it as you’ve learned that you need more information (more numbers solved) in order to solve that area of the puzzle.
For the overly curious only: for the purposes of using BLOCK OUTS, Column+Blocks 1,2, and 3 are the only configurations you can use and still successfully apply this technique. In other words, you can’t use the last Column from Column+Block 1 and then the first 2 from Column+Block 2 and call that a Column Block. Why? The logic will not work because the rule that you can have only one occurrence of the numbers 1 through 9 in each Row, Column, and Block do not apply once you cross a Column Block boundary.
NEXT UP: Lesson #7. Housekeeping
Copyright 2006 Gary Ward All Rights Reserved |