Sudoku HowTo

# Cross Hatching

Cross Hatching uses values already placed in the puzzle to identify locations in a box, row or column for a new value.

Generally, cross hatching is done on boxes first but does not have to be.

In the Cross Hatching example in Figure 1 the highlighted cell in box 4 shows the only place the value 2 can be placed in box 4.

The value 2 cannot be placed in rows 4 or 5, or column 2 because there is already a value 2 in these units. The only empty cell in box 4 that is not in rows 4 or 5, or column 2 is the highlighted cell.

Scanning each box one value at a time will usually identify the most cross hatching opportunities.

You are really looking for a single cell in a unit that contains a particular candidate. When there is only one cell in a unit that contains a particular candidate, that candidate can be inserted as the solution for that cell.

Cross Hatching can also be applied to rows or columns. In the example in Figure 2, the value 4 can only be placed in the highlighted cell in column 7. All other empty cells in column 7 cannot be the value 4 because of the value 4 already in rows 1,7 and 8 and/or the value 4 in box 9.

In this case, either the value 4 in row 7 or the value 4 in box 9 can be used to remove the cell in row 7 column 7 as a possible location for the value 4. Similarly, the value 4 in row 8 or the value 4 in box 9 can be used to remove the cell in row 8 column 7 as a possible location for the value 4.

17 February 2021
by hi!
RE: Comments and feedback for crossHatching

gud job!
2 February 2021
by Charles King
RE: Comments and feedback for crossHatching

The first example is very good and correct.

Example 2 - Re: Atul Narain's comment, he is correct that the logic used in the text makes little sense. Here is the correct logic.
R3-C7 has possible candidates 489.
R3-C9 has possible candidates 3489.
Whenever there is a "unique value" in a row, column, or block, THAT is the answer to the cell. The term "hatching" is better replaced with "uniqueness."
C7 has only one(1) possible candidate 4; so R3-C7 is a 4 (correct logic).
R3 has multiple 4 candidates; C9 has multiple 4 candidates.
2 February 2021
by Charles King
RE: Comments and feedback for crossHatching

The first example is very good and correct.

Example 2 - Re: Atul Narain's comment, he is correct that the logic used in the text makes little sense. Here is the correct logic.
R3-C7 has possible candidates 489.
R3-C9 has possible candidates 3489.
Whenever there is a "unique value" in a row, column, or block, THAT is the answer to the cell. The term "hatching" is better replaced with "uniqueness."
C7 has only one(1) possible candidate 4; so R3-C7 is a 4 (correct logic).
R3 has multiple 4 candidates; C9 has multiple 4 candidates.
2 February 2021
by Charles King
RE: Comments and feedback for crossHatching

The first example is very good and correct.

Example 2 - Re: Atul Narain's comment, he is correct that the logic used in the text makes little sense. Here is the correct logic.
R3-C7 has possible candidates 489.
R3-C9 has possible candidates 3489.
Whenever there is a "unique value" in a row, column, or block, THAT is the answer to the cell. The term "hatching" is better replaced with "uniqueness."
C7 has only one(1) possible candidate 4; so R3-C7 is a 4 (correct logic).
R3 has multiple 4 candidates; C9 has multiple 4 candidates.
2 February 2021
by Charles King
RE: Comments and feedback for crossHatching

The first example is very good and correct.

Re: Atul Narain's comment, he is correct that the logic used in the text makes little sense. Here is the correct logic.
R3-C7 has possible candidates 489.
R3-C9 has possible candidates 3489.
Whenever there is a "unique value" in a row, column, or block, THAT is the answer to the cell.
C7 has only one(1) possible candidate 4; so R3-C7 is a 4.
R3 has multiple 4 candidates; C9 has multiple 4 candidates.
30 January 2021
by Anonymous
RE: Comments and feedback for crossHatching

Thanks I understand it much better now!
16 June 2020
by John
RE: Comments and feedback for crossHatching

If you look down column 6 there is a 4 already in every every row except for row 3. There has to be a 4 in column 6 and the only empty row that does not already have a 4 in it is row 3. Once the 4 is in row 3 column 6 it cannot be in row 3 column 9
16 June 2020
by Atul Narain
RE: Comments and feedback for crossHatching

Just wanted to know why 4 cannot be inserted in the 3rd row column 9 marked 389
16 June 2020
by Atul Narain
RE: Comments and feedback for crossHatching

Just wanted to know why 4 cannot be inserted in the 3rd row column 9 marked 389
19 August 2019
by Patricia Byron
RE: Comments and feedback for crossHatching

Just a newbie but love the way you describe things. I am quite dyslexic ... but enjoy your remarkable instructions and clarity. Thank you for all the work and sharing.
16 July 2019
by Sourav pramanik
RE: Comments and feedback for crossHatching

I am not understanding it.

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