Pattern: Gate Pattern


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Introduction

The gate pattern is useful for sometimes finding numbers but you will at least know in which row or column the number goes in. If conditions are right you can solve numbers using this pattern.

Details

The gate pattern exists when there are two cells in a box in the same row or column and the third cell in the row or column is empty. It doesn't matter where in the box the populated cells are as long as

  1. They are in the same row or column and
  2. There are two populated cells and one empty cell.

When this condition exists you have a gate pattern. In order for the gate pattern to be useful you also need to have

  1. One or more numbers, in the same row or column as the gate, that are outside of the box the gate is in and
  2. The same number(s) in the corresponding row or column.
Sudoku grid partially filled to show an example of the gate pattern
Figure 1

Finding a 9 in box 2

Look at figure 1 above. In box 2 there is a gate in row 1 (the row with 4 and 5 in it). The middle unpopulated cell in column 5 is a gate. Look down column 5 and you see a 2 and 9 that "go through" the gate.

There are no 2s in the rows to the left or right box of box 2 so the 2 in column 5 doesn't help. But the 9 in column 5 has a corresponding 9 in row 2 in box 1. That means that the 9 in box 2 must be in row 3.

In this case there is also a 9 in column 4 which constrains the 9 in box 2 to r3c6. So in this example the gate pattern found a 9 for us!

Finding a 6 in box 4

Now look at box 4. The numbers 3 and 4 are already in the box in column 1. If you look at row 4 the numbers 4, 6 and 8 "go through" the gate. Focus on the 6 in row 4. There is also a 6 in column 2 in box 1. This tells us that the 6 in box 4 must be in column 3. And since row 6 already has a 6 in it the 6 in box 4 must be in row 5 at r5c3.

Video about the gate pattern
Watch this video for more gate info and examples of the gate pattern



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