The wall is a simple pattern. It is where three numbers are already in a row or column within a box. Figure 1 shows examples of wall patterns.
The image above shows several wall patterns in different locations. In box 1 the 598 wall is in the middle column (column 2). Box 2 has a wall in column 6, which is on the right hand side of the box. Boxes 4 and 7 have walls in rows, in the middle row of box 4 and the bottom row of box 7. You get the idea. Now how can these help us?
Figure 2 shows how you can benefit from this pattern.
Let's look at each of the red numbers, one at a time. Observe the red 3. It is in column 3 and if you look at box 1 with the 598 wall you will notice that the 3 can only fit in column 1, rows 1 or 2. At the same time, in box 7 you'll notice that a 3 can only fit in column 2 in that box because of the wall in box 1.
Now look at the red 2. A 2 can only fit in column 3 in box 1 because of the 598 wall. And a 2 can only fit in column 2 in box 4 because of the same wall.
Look at the red 1. Since there is already a 1 in box 2 in the 123 wall box 8 can only have a 1 in column 4, either in row 8 or 9 (because of the 1 in box 9). Let's keep looking at that because the 1 in box 9's 183 wall means that a 1 in box 7 can only be in row 8 because of the 749 wall. Because of that we can place the 1 in box 8 (we know that the 1 must go in r9c4).
Now let's examine the red 5 and 9. We know we can place a 5 in box 4 in cell r6c1 because of the 876 wall in box 4 and the 5 in the 598 wall in box 1. Once the 5 is placed in box 4, the 9 can only go in r4c1 in box 4.
Observe box 9 in figure 2. It has a double wall 295 and 183. When you see this you will know a) the remaining three numbers in the middle column are 4, 6 and 7, b) that the 5 and 9 in box 3 go in column 9, and c) that the 3 in box 6 goes in column 7 and the 3 in box 3 goes in column 8. This is because the red 3 in row 6 "completes" the 59 wall in box 6 so you know which column the three goes in in box 6.
The 3 example in box 6 is what is called "hidden patterns" or in this case a "hidden wall." More on hidden patterns will be coming soon on a page specific to hidden patterns. They can be very powerful.
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