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Tap every digit that could go between the 3 and the 6.
Select all that apply
Level 3 · Lines
How to solve between lines
Digits on the line sit strictly between the two circled digits at its ends.
A between line joins two circles. Every digit on the line must be strictly greater than the smaller circle and strictly less than the larger one. Either end can hold the bigger digit.
The circles set a range, and the length of the line decides how wide that range has to be. Both the circles and the line cells get narrower as you learn more about either.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Digits on a line between two circles must be strictly between the circled digits.
- Between lines.
Worth memorizing
- The circles can’t be consecutive if any cell sits between them.
- A long line needs its circles far apart: three cells between need a gap of at least four.
Solving tips
Circles can't be consecutive
If any cell sits between the circles, they can't be equal or one apart. A 4 and a 5 leave no digit strictly between them.
Length sets the gap
Three line cells in one box need three different digits, so the circles must be at least 4 apart. Circles of 2 and 6 fit exactly 3, 4 and 5.
Keep 1 and 9 off
Nothing is below 1 or above 9, so line cells are never 1 or 9. Those digits can only go in the circles.
Push the far circle
If one circle is 3 and the line has three cells in one box, the line needs three digits above 3. The other circle is at least 7.
A worked example: four line cells in one row
A between line has two circles and four line cells, all six in the same row. The row also has a 2, a 3 and a 9 in cells off the line.
- The four line cells share a row, so they hold four different digits. Four digits strictly between the circles need a gap of at least 5 between the circles.
- The row's 9 is off the line, so the higher circle is at most 8. With a gap of at least 5, the lower circle is at most 3.
- The row's 2 and 3 are off the line too. So the lower circle is 1.
- Now the line cells come from 2 up to one less than the higher circle, without the 2 and 3 in the row. If the higher circle is 6, only 4 and 5 are left. If it is 7, only 4, 5 and 6 are left. Neither gives four digits, so the higher circle is 8.
- The circles are 1 and 8, and the line holds 4, 5, 6 and 7 in some order. Which circle is 1 is still open. That comes from the columns through the two circles.
Practice
Reference table
| Line cells that see each other | Smallest circle gap | Possible circle pairs | Lower circle | Higher circle |
|---|---|---|---|---|
| 1 | 2 | 28 | 1 to 7 | 3 to 9 |
| 2 | 3 | 21 | 1 to 6 | 4 to 9 |
| 3 | 4 | 15 | 1 to 5 | 5 to 9 |
| 4 | 5 | 10 | 1 to 4 | 6 to 9 |
| 5 | 6 | 6 | 1 to 3 | 7 to 9 |
| 6 | 7 | 3 | 1 to 2 | 8 to 9 |
| 7 | 8 | 1 | 1 | 9 |
Going deeper
Count only cells that see each other
The circle gap depends on how many line cells must be different. Cells in different rows, columns and boxes can repeat, so a long line spread over several boxes may need a smaller gap than its length suggests.
Find the largest group of line cells that all share one row, column or box. That group sets the minimum gap. A 5-cell line with 3 cells in one box and 2 in the next needs a gap of at least 4, since the three cells in one box need three different digits. The table on this page lists gaps for each group size. Two cells in different boxes can still share a row or column, so check rows and columns as well as boxes when you look for the largest group.
Working back from the line to the circles
Line digits also limit the circles. A 2 on the line means one circle is 1, since 1 is the only digit below 2. An 8 on the line means one circle is 9.
If the line holds both a 3 and a 7, the lower circle is 1 or 2 and the higher circle is 8 or 9. Look for the smallest and largest digits the line could hold, and push the circles outside them. A 5 on the line is a useful case. It means one circle is 4 or lower and the other is 6 or higher, so neither circle can be 5. At the other extreme, a line with 7 cells that all see each other must have circles of 1 and 9, and its cells hold 2 to 8.
Deciding which circle is higher
The rule works in both directions, so the circles give no hint by their position. Find it from the grid. For example, if the lower circle must be 1, 2 or 3, and one circle's row already has 1, 2 and 3, that circle is the higher one.
Once one circle is known to be the lower one, every limit on the line cells becomes a limit on it, and the same goes for the higher circle. A 9 is another quick test. If one circle's row, column or box already holds a 9, and the line needs a higher circle of 9, the other circle takes it.
Common mistakes
Assuming the left circle is smaller
Either circle can be the higher one. Solve for both options until the grid rules one out.
Letting a line digit equal a circle
The line digits must be strictly between the circles. A line with circles of 3 and 7 can hold 4, 5 and 6 only. It can't hold a 3 or a 7.
Counting every cell on a long line
Only cells that see each other must differ. Counting every cell of a line that crosses boxes can make you think the circles need a bigger gap than they do, and you may remove legal digits from the circles.
In mixed-rule puzzles
Between lines sit well next to thermos and renbans. When a renban is also a between line, the circles sit anywhere outside the run. A 3-cell renban of 4, 5, 6 on a between line needs one circle from 1 to 3 and the other from 7 to 9. A thermo cell on a between line must satisfy both the thermo range and the circle range, so take the overlap. Kropki dots on the circles can help settle which circle is higher. For example, a black dot between the lower circle and a line cell means the line cell is double the circle, which is only possible for some circle values.
What the video shows
- Digits on the line sit strictly between the two circled digits.
- The circles hold 2 and 7.
- 8 is outside 2 to 7.
- 5 and 4 both sit between 2 and 7.
Questions solvers ask
What is a between line in sudoku?
A line with a circle at each end. Every digit on the line must be strictly between the two circled digits.
Which circle on a between line is bigger?
Either one. The rule works in both directions, so you find out which end is higher while solving.
Can a digit on a between line equal a circle?
No. The line digits must be strictly between, so they can't match either circle.
Can digits repeat on a between line?
Yes, if the cells don't share a row, column or box.
Can a circle on a between line be 5?
Yes. It can be the lower circle with a higher one above it, or the higher circle with a lower one below it. The line cells then sit on the other side of 5.
Do between lines have to be straight?
No. A between line can bend. The rule depends only on the circles at its two ends and the cells along it.
Can two between lines share a circle?
Yes. The shared circle must work for both lines. It can be the lower circle for one line and the higher circle for the other.
Record Highs
Toy Hidden Between Lines (Nala’s Adventures #2)
RAT RUN 24: Between You and Me
Wheels
Target Practice
Read Between the Lines (Build Your Own Puzzle)