Sudoku Pattern Adjacency

If you have been able to memorize all the patterns I shared in my post about Sudoku Square Patterns, then solving some Sudoku puzzles should be a breeze.

The non-diagonal Sudoku Square Patterns I shared were:

1.  123
2.  345
3.  678
4.  135
5.  357
6.  316 (which I called John 3:16)
7.  196
8.  145
9.  945

In the figure below, I simply drop the Non-Diagonal Pattern (NDP) labels so that it is easier to visualize.

 

Based on the diagram, we can see that a 678 NDP, a 135 NDP, and a 357 NDP will always be in the same row or column. Shifting of rows and columns are possible. So the 678 - 135 - 357 row can switch places with the 145 - 945 - 123 row. The 135 - 316 - 945 column can shift positions with the 357 - 196 - 123 column. The square patterns act like jigsaw pieces in a 3 by 3 jigsaw puzzle. If you can figure out the location of two pieces, then you can pretty much figure out the location of the rest of the pieces.

 

 

Sudoku Square Pattern 945 Horizontal

Another favorite pattern of mine is what I call the 945 Horizontal Pattern or 945 Non-diagonal Pattern. You can see a sample of it below.

 

I usually remember it as 945, 138, 276. And again, you can switch the order of rows or columns. And 945 can be vertical or horizontal. But once you find the 945 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Pattern 145 Horizontal

Another favorite pattern of mine is what I call the 145 Horizontal Pattern or 145 Non-diagonal Pattern. You can see a sample of it below.

 

I usually remember it as 145, 298, 673. And again, you can switch the order of rows or columns. And 145 can be vertical or horizontal. But once you find the 145 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Pattern 196 Horizontal

Another favorite pattern of mine is what I call the 196 Horizontal Pattern or 196 Non-diagonal Pattern. You can see a sample of it below.

I usually remember it as 196, 832, 745. And again, you can switch the order of rows or columns. And 196 can be vertical or horizontal. But once you find the 196 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Patterns 316 Horizontal

Another favorite pattern of mine is what I call the 316 Horizontal Pattern or 316 Non-diagonal Pattern. As a Christian, the verse John 3:16 is very memorable for me since I memorized it in Sunday School. The verse states:

For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.

You can see a sample of the pattern below.

I usually remember it as 316, 489, 752. And again, you can switch the order of rows or columns. And 316 can be vertical or horizontal. But once you find the 316 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Patterns 678 Horizontal

Another favorite pattern of mine is what I call the 678 Horizontal Pattern or 678 Non-diagonal Pattern. You can see a sample of it below.

I usually remember it as 678, 245, 931. And again, you can switch the order of rows or columns. And 678 can be vertical or horizontal. But once you find the 678 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Pattern 345 Horizontal

Another favorite pattern of mine is what I call the 345 Horizontal Pattern or 345 Non-diagonal Pattern. You can see a sample of it below.

I usually remember it as 345, 726, 891. And again, you can switch the order of rows or columns. And 345 can be vertical or horizontal. But once you find the 345 sequence in a row or column, then the entire square pattern should hold.

This square also has another Bonus sequence and I think you can easily spot it from above. If you guessed the 123 Diagonal Pattern, you are correct! As long as I see a 123 diagonal in any 3 by 3 square, I immediately know that I am dealing with a 345 Non-diagonal Pattern.

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Sudoku Square Patterns 357 Horizontal Pattern

Another favorite pattern of mine is what I call the 357 Horizontal Pattern or 357 Non-diagonal Pattern. You can see a sample of it below.

I usually remember it as 357, 694, 812. And again, you can switch the order of rows or columns. And 357 can be vertical or horizontal. But once you find the 357 sequence in a row or column, then the entire square pattern should hold.

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Sudoku Square Patterns 135 Horizontal

Another favorite pattern of mine is what I call the 135 Horizontal Pattern or the 135 Non-diagonal Pattern. You can see a sample of it below.

I usually remember it as 135, 946, 728. And again, you can switch the order of rows or columns. And 135 can be vertical or horizontal. But once you find the 135 sequence in a row or column, then the entire square pattern should hold.

This pattern is also what I call a Bonus pattern because it has another easy-to-remember sequence of number within it. Can you spot the numbers?

If you guessed 234, then you are correct. I could memorize another set of numbers as 234, 856, 719, but instead of doing that, I know that if I spot the sequence 234 in a row or column, then I'm dealing with a 135 Horizontal Square Pattern.

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Sudoku Square Patterns

I have been playing Sudoku for many years and what I noticed was there were certain 3 by 3 square patterns that seem to come up in every new game. Sudoku is made up of 9 by 9 squares or can also say, Sudoku is made up of nine 3 by 3 squares. And the patterns that I have noticed are in the 3 by 3 squares. Memorizing these patterns can help speed up your puzzle completion time.

Here is an example of a 3 by 3 square pattern.

 

This pattern is one of my favorites and I call it the 123 Horizontal Pattern. I usually memorize this pattern as 123, 589, 746, if you read each row from top to bottom. Once I spot any of these combinations in a row or column within a 3 by 3 square, then I can most likely complete the entire 3 by 3 square.

Just look for any 3 by 3 square with one row or column with the number 1, 2, and 3. It doesn't even matter if you reverse the order, or switch the order of 1, 2, and 3. For example, the above pattern can appear as 321, 985, 647 if you switch the positions of the first and third column. Or it can appear as 231, 895, 467 if you again switch the first column with the second column. Or you could switch the order of rows and come up with a pattern like 589, 746, 123. As long as you identify that the 123 numbers are in the same row or column, then you can expect the other numbers to follow the pattern 123, 589, 746.

But maybe I should call it the 1 2 3 Non-diagonal Pattern instead because this pattern will still hold even if 123 is vertical. I have noticed that there are diagonal patterns, too. However, spotting them might not be as easy as looking for horizontal or vertical number sequences.

I have tried to come up with patterns that are easy to remember such as three successive numbers or three successive odd or even numbers. Below is a list of the patterns I have identified so far: (a.k.a. stands for also known as).

• 123 Non-diagonal Pattern (shown above) a.k.a 369 Non-diagonal Pattern
  
• 345 Non-diagonal Pattern a.k.a. 123 Diagonal Pattern
• 678 Non-diagonal Pattern  
  
• 135 Non-diagonal Pattern a.k.a. 234 Non-diagonal Pattern
  
• 357 Non-diagonal Pattern
• John 3:16 Non-diagonal Pattern 
• 196 Non-diagonal Pattern a.k.a 135 Diagonal Pattern
• 145 Non-diagonal Pattern
  
• 945 Non-diagonal Pattern
  

Hopefully, these patterns will help you out in solving Sudoku faster. Who knows, in the future, you, too, might come up with your own favorite patterns which you'll hopefully share with other players in the world. 

Once you have been able to memorize all these patterns, then you might want to try your hand at Sudoku Pattern Adjacency which is another technique I share to try and speed up your Sudoku puzzle solving time.