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Lesson #9. If you can’t BLOCK ‘em OUT, try to at least PIN ‘em DOWN
Go TEAM!
Well, I’d drop the sports language completely if it weren’t for the fact that PIN DOWNS are actually related to TEAMS and are integral to working with them.
Let’s start with the obvious question: What’s a PIN DOWN? I’ll illustrate it in just a moment but here’s the general idea: Sometimes you can’t determine the exact Cell where a number goes but you can PIN it DOWN to within a few cells. Why is that important? Because it often enables you to remove any other occurrences of the number from other Cells in the associated Block. And as always, the more numbers you can remove from the grid, the closer you are to solving the puzzle.
Take a look at this Sudoku puzzle fragment. (Again, just a fragment for illustration purposes.)
In the first Row, there’s a TEAM of 3 composed of the numbers 5-7-8 divided up into three cells of (5,8), (5,7), and (7,8). To refresh what this means, I’ll remind you that the numbers 5-7-8 can only be placed in these locations within Row 1. Now here’s the catch. Note that the number 7 occurs twice and both occurrences are in the right block.
This means that for Row 1, the 7 must be placed in either the (5,7) Cell or the (7,8) Cell. Simple enough. But, both of these Cells are located in the same Block. Therefore, we’ve are now able to PIN DOWN the 7 to one of these Cells in Row 1 of this Block. That means that all of the other 7s in that Block can be erased. Our Sudoku puzzle fragment now looks like this.
Note that we’ve removed three 7s (two in Row 2 and one in Row 3.) Now this may not seem like much because we weren’t able to actually solve any of the Cells but remember that anytime you can remove some numbers from grid, you’re that much closer to solving the puzzle.
Here’s another PIN DOWN example, this time using Columns instead of Rows. Pay particular attention to the numbers in Column 2 (the middle columns.)
Notice that in Column 2, the number 4 is found only in the middle Block.
This means that in Column 2, we’ve been able to PIN DOWN the number 4 to the two Cells in the middle Block (3-4-5-8 and 4-5-8.) This means that we can erase the 4s in the two adjacent cells yielding the following:
While this might not seem like a big change just remember that any time that you can eliminate numbers from the grid, you’re getting closer to solving the puzzle.
Also, notice we didn’t have to identify a TEAM. Just the fact that the 4s were isolated in the middle Block within Column 2 was enough to allow us to apply the PIN DOWN technique.
Checklist for using the PIN DOWN technique:
- Examine each Row and Column and look for instances where a particular number is isolated within a Block that intersects the Row or Column - If you can’t find one, check to see if there’s a TEAM of numbers of any size that has one it its numbers isolated within an intersecting Block - If either of these conditions is true, you can then establish a PIN DOWN for that number within that Block and erase all other occurrences of that number from the other Cells in the Block.
One last thought: To me, learning how to use PIN DOWNS made the biggest difference in my ability to solve difficult Sudoku puzzles. Once you learn to use it successfully, let me know if you agree that it is a great way to crack the harder Sudoku Puzzles.
NEXT UP: Lesson #10. SHARED PAIRS
Copyright 2006 Gary Ward All Rights Reserved |