Omission Walkthrough
Omission (Locked Candidates) occurs when, within a box, a candidate is confined to a single row or column. The digit must fall on that line, so it can be eliminated from the rest of that row or column.
Below are 3 positions from real puzzles, each captured when the solver first needs this move. Find the pattern on each before-board yourself, then read the notes and check the after-board, where removed candidates are struck out in red and solved cells shown in green.
Example 1: Omission can be applied between Row 5 and Block 6
Two separate Omissions on the digit 7 fire in this step, and the after-image shows both. First, the one the hint names: in box 4, every cell that can still hold a 7 is in row 5 (r5c1 and r5c3), so row 5 gets its 7 inside box 4, and 7 is struck from r5c8 and r5c9 in box 6. The second runs vertically. In box 9 the 7 is confined to column 8, which removes it from r3c8 and r4c8 further up that column. That is four eliminations from two patterns. Once one Omission turns up, check the same digit in every other box.
Example 2: Omission can be applied between Row 8 and Block 7
Follow the 1. Inside box 8 it can only go in r8c4 or r8c5, both in row 8, so row 8 gets its 1 inside box 8 and nowhere else. That removes 1 from r8c2 and r8c3 over in box 7. r8c3 had only {1,9}, so the elimination solves it as 9. Row 7 gives the same result from the other side, because there the 1 is confined to r7c2 and r7c3, both in box 7. Two different routes to the same deduction are common with Omission, and either one is enough.
Example 3: Omission can be applied between Row 6 and Block 5
This step is busy. The solver keeps applying Omissions until a cell is solved, and here it finds five of them on four different digits, which is why seven candidates disappear. The one the hint names is the 7 in box 4: it is confined to r6c1 and r6c3, so it is struck from r6c5 in box 5. Try to find the other four yourself. Column 5 keeps its 4 inside box 5, which clears r4c4 and r4c6. Box 8 keeps its 7 in column 4, which clears r4c4 again. Box 3 has 1 only in column 9, which clears r7c9, r8c9 and r9c9. Last, box 5 has 8 only in column 5, which removes it from r2c5 and solves that cell as 5.
Why the deduction is valid
Omission — also called Locked Candidates, or pointing and claiming — exploits the overlap between a box and a line. If every cell in a box that could hold a digit lies in the same row, then that digit is somewhere in that row no matter which of those cells it turns out to be, so it can be eliminated from the rest of the row outside the box. The same argument runs in reverse: if a digit within a row can only appear in the cells that fall inside one box, it is eliminated from the rest of that box.
How to spot a Omission on your own board
- For each box, take one missing digit and mark every cell that could hold it. If they all share a row or column, you have a pointing elimination along that line.
- For the reverse direction, take a row or column and a digit missing from it. If the digit is confined to the two or three cells the line shares with one box, clear it from the rest of that box.
- Two cells in line is the common case; three in line inside a single box is the strongest version and clears six cells at once.
Common mistakes
- Applying the elimination to the wrong side of the overlap. Pointing clears the line outside the box; claiming clears the box outside the line. Deleting inside the intersection is always wrong.
- Only ever checking rows. Half of all Omissions run down columns, and solvers who scan horizontally by habit find roughly half the pattern.
What to do next
Omission is the highest-yield technique per unit of effort on medium and hard puzzles, and it is usually the rung people are missing when a puzzle stalls. Once the line is cleared, look for Hidden Singles in it — the elimination often leaves a digit with exactly one home.