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Tap every digit that could go next to the 5 in this row.
Select all that apply
Level 4 · Whole-grid rules
How to solve non-consecutive sudoku
Cells that share an edge can’t hold digits that are one apart.
Non-consecutive sudoku adds one rule to the whole grid. Two cells that share an edge can't hold digits that are one apart, such as 3 and 4. Cells that touch only at a corner are not affected.
The rule applies to every pair of neighbors, so it cuts candidates everywhere. Digits from 2 to 8 have two consecutive partners, and 1 and 9 have only one.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Orthogonally adjacent cells cannot contain consecutive digits.
- Non-consecutive.
Worth memorizing
- A 5 rules out 4 and 6 in all four neighbors.
- Diagonal neighbors are fine.
Solving tips
One digit clears two
A 5 rules out 4 and 6 in every cell that shares an edge with it. A 1 only rules out 2, and a 9 only rules out 8.
Consecutive pairs block both
A cell that must be 3 or 4 keeps both 3 and 4 out of its four neighbors. Whichever it turns out to be, the neighbors can't match it or be one away.
Only check four cells
Diagonal neighbors can hold consecutive digits, so a 4 and a 5 may touch at a corner. Look only at the cells above, below, left and right.
Read it like Kropki
Non-consecutive works like a Kropki puzzle with no white dots where all dots are given. If a puzzle mixes the two, a white dot marks the only places neighbors can be one apart.
A worked example: a cell between a 2 and an 8
Non-consecutive is on. We name cells by row and column, so row 1, column 1 is r1c1. r1c1 holds 2 and r1c3 holds 8. The cell between them, r1c2, is empty. The cell below it, r2c2, holds 4.
- r1c2 shares row 1 with the 2 and the 8. So it can't be 2 or 8.
- r1c2 shares an edge with the 2 in r1c1. So it can't be 1 or 3.
- r1c2 also shares an edge with the 8 in r1c3. So it can't be 7 or 9. That leaves 4, 5 and 6.
- r2c2 is directly below and holds 4. It shares an edge with r1c2, so r1c2 can't be 3 or 5. It also shares column 2, so r1c2 can't be 4. Only 6 is left.
- Check it. The 6 is 4 away from the 2, 2 away from the 8, and 2 away from the 4. No pair is one apart, so r1c2 = 6.
Practice
Reference table
| Digit | Can't share an edge with it | Can share an edge with it |
|---|---|---|
| 1 | 2 | 3, 4, 5, 6, 7, 8, 9 |
| 2 | 1, 3 | 4, 5, 6, 7, 8, 9 |
| 3 | 2, 4 | 1, 5, 6, 7, 8, 9 |
| 4 | 3, 5 | 1, 2, 6, 7, 8, 9 |
| 5 | 4, 6 | 1, 2, 3, 7, 8, 9 |
| 6 | 5, 7 | 1, 2, 3, 4, 8, 9 |
| 7 | 6, 8 | 1, 2, 3, 4, 5, 9 |
| 8 | 7, 9 | 1, 2, 3, 4, 5, 6 |
| 9 | 8 | 1, 2, 3, 4, 5, 6, 7 |
Going deeper
Cells with two or three candidates
You don't need a placed digit to remove candidates. Look at what every option for a cell has in common. If a cell is 4 or 6, each option rules out 5 from its neighbors. So all four neighbors lose 5, even before you know which one it is.
The same works for bigger sets. A cell that is 4, 5 or 6 rules out 5 in its neighbors, since 5 is either the same digit or one away in every case. A cell that is 3 or 5 rules out 4. Look for the digit that every option bans.
The ends of the range work too. A cell that is 1 or 2 removes both 1 and 2 from its neighbors. A cell that is 8 or 9 removes both 8 and 9.
Three digits in a row can't all be consecutive
Three cells in a line, such as r1c1, r1c2 and r1c3, can't hold three consecutive digits like 3, 4 and 5. The middle cell touches both ends. Whatever goes in the middle, it is one away from at least one of the other two. For example, 3, 5, 4 fails because the 5 and the 4 touch. The same holds for three cells in a column.
Use this when a row segment must hold a set of close digits. If a row still needs 3, 4 and 5, and the only empty cells are three side by side, a digit placed earlier is wrong. More often, it tells you those three digits must be spread out with other digits between them.
Why 1 and 9 are easier to place
Digits from 2 to 8 rule out two digits in every neighbor. 1 and 9 rule out only one. So 1 and 9 have more room to fit, and middle digits like 5 usually run out of space first.
When you are stuck, pick a middle digit and scan where it can still go in each box. Its options shrink faster than the options for 1 or 9.
Position matters too. A corner cell has two neighbors that share an edge with it, an edge cell has three, and every other cell has four. A digit in r1c1 limits just two cells by this rule, while a digit near the middle of the grid limits four.
Common mistakes
Checking diagonal neighbors
The rule covers only the four cells above, below, left and right. A 4 and a 5 may touch at a corner. Crossing off diagonal cells removes candidates that are still possible.
Treating 9 and 1 as consecutive
Consecutive means one apart. 9 and 1 are eight apart, so they can sit side by side. The digits don't wrap around unless the puzzle says so.
Waiting for placed digits
Beginners often use the rule only after a cell is filled. Much of the work comes from candidates. A cell that is 4 or 6 already removes 5 from its neighbors.
In mixed-rule puzzles
Non-consecutive changes other clues in useful ways. On a thermometer, each cell must be bigger than the one before, and when the cells share edges each step must now be at least 2. A five-cell thermometer along edges must be 1, 3, 5, 7, 9 in that order. German whispers already need neighbors at least 5 apart, so the rule adds nothing along the line itself. With Kropki dots, puzzles often mark white dots where neighbors are one apart and use the non-consecutive rule everywhere else. Check the wording, since the dots and the rule must not contradict each other. With anti-king, the same digit can't touch at all, and edge neighbors also can't be one apart.
What the video shows
- Cells side by side can’t hold consecutive digits.
- 4 and 5 are consecutive.
- 4, 7, 2: no neighbors are one apart.
Questions solvers ask
What is non-consecutive sudoku?
A sudoku where cells that share an edge can't contain digits one apart, like 6 and 7.
Do diagonal cells count in non-consecutive sudoku?
No. Only the four cells that share an edge with a cell are affected.
Are 1 and 9 consecutive in sudoku?
No. Consecutive means one apart, so 1 and 9 can sit side by side unless the puzzle says otherwise.
How is non-consecutive sudoku related to Kropki?
It works like a Kropki puzzle with no white dots and a rule that all dots are given. No two neighbors can be one apart.
What does orthogonally adjacent mean in sudoku?
It means two cells share an edge: one is directly above, below, left or right of the other. Cells that touch only at a corner are not orthogonally adjacent.
How many digits can go next to a 5 in non-consecutive sudoku?
Six: 1, 2, 3, 7, 8 and 9. The 4 and the 6 are one away, and the 5 can't repeat in its own row or column.
Can three consecutive digits sit in a row in non-consecutive sudoku?
Not in three cells side by side. They can appear in the same row if other digits sit between them.
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