Consecutive and XV Sudoku: How to Solve Edge Clues
Consecutive Sudoku and XV Sudoku both put their clues on the edge between two neighbouring cells. They look different, but the habit they teach is the same: read a pair of cells as one small arithmetic statement.
In Consecutive Sudoku, a bar means the two digits differ by exactly 1. In XV Sudoku, an X means the two digits add to 10 and a V means they add to 5.
The rules that do not change
Every row, column, and 3×3 box still contains 1 to 9 once each. Start with ordinary Sudoku when those rules are new, then come back to the edges once a candidate list is familiar.
Consecutive: use the ends first
A bar beside a 1 must lead to a 2. A bar beside a 9 must lead to an 8. Digits in the middle have two neighbours — a 5 can pair with a 4 or a 6 — so the ends give the fastest placements.
Here a 9 near the bottom of the board has a bar running up out of it. Its partner would have to be 8 or 10, and 10 is not a digit.
The rest is ordinary Sudoku. If a barred cell can only be 4 or 6, look at its partner’s row, column, and box. One of those two values often cannot fit there.
XV: count pairs, then remove them
An X has four unordered pairs: 1+9, 2+8, 3+7, and 4+6. A V has two: 1+4 and 2+3. A V is therefore the sharper clue, especially when one cell is known.
The 3 on this board is touched twice. The V on its right needs a 2 to reach five; the X below it needs a 7 to reach ten.
If a V touches a 4, its partner is 1. If an X touches an 8, its partner is 2. These short calculations are simple; their value comes from carrying the result back into the row, column, and box.
Whether a blank edge means anything depends on the puzzle
A mark is a statement about the pair it sits on. A blank edge, by default, is not a statement at all — it means the puzzle told you nothing about those two cells, not that the relationship is absent.
Some puzzles adopt a stronger convention called complete marking: every relationship that applies is drawn. Only then does absence become information. No bar between two cells means those digits do not differ by 1; no X or V means the pair adds to neither ten nor five. A puzzle using that convention has to say so in its rules. If the rules do not mention it, assume it is not in force.
The difference is worth the care. Under complete marking the blank edges outnumber the marked ones several times over, and each one is a constraint, so the negative deductions can carry most of the solve. Apply those same deductions to a puzzle that draws only selected clues and you will reach contradictions that look like your own arithmetic mistakes.
Both boards below are completely marked, and their data says so. The highlighted cell has only 2 and 7 left in it. The 3 underneath it carries no bar, so the 2 is impossible and the cell is 7 without any further work.
XV gives the same deduction from the other direction, on a board marked the same way. This cell is also down to 2 and 7. An X would have been drawn if the pair added to ten, and there is none, so the 8 next door has already removed the 2.
On those two boards the missing sign carries information instead of merely leaving the grid blank.
Sudoku Fog does not use complete marking. A Consecutive or XV board generated in the app draws only some of the relationships that apply, so a blank edge there tells you nothing, and every deduction has to start from a mark you can see. That is the ordinary case, and it is the one to assume anywhere the rules are silent.
Try it
Both practice boards below are completely marked, like the examples above, so the negative deductions are available on them — unlike the boards the app generates.
Consecutive first. Look for the 1s and 9s: a bar beside either has one partner and no choice to make.
Then XV. Work the V clues before the X clues, because there are only two ways to make five and four ways to make ten.
Where to go next
Kropki puts its clues on the same cell edges, using dots rather than bars and letters, and raises the same question about what a blank edge means. Arrow keeps the arithmetic but moves it off the edge and onto a path across the grid.
If you want the version where most of the grid is hidden while you solve, fog of war Sudoku is that. Everything published so far is on the Learn index.
Sudoku Fog is on Android — What Sudoku Fog is, Get it on Google Play.