XV Sudoku: Rules & How to Solve
X marks a pair summing to 10, V marks a pair summing to 5. A clean additive variant hiding on the cell borders.
The rule
An X between two cells means they sum to 10; a V means they sum to 5. (XV combines the Roman numerals: X = 10, V = 5.) Many puzzles also use a negative constraint — if no X or V is shown, the pair sums to neither.
The complete X and V pair table
There are very few options, which is what makes XV so sharp once you memorise them.
| Marker | Sum | Every possible pair |
|---|---|---|
| V | 5 | {1,4}, {2,3} |
| X | 10 | {1,9}, {2,8}, {3,7}, {4,6} |
Two subtleties matter. A V can never be {5,0} because there is no 0, and an X can never be {5,5} because the two cells are adjacent and would repeat a digit. So 5 never appears in an X or V pair at all — the same quirk that keeps 5 off a german whispers line.
The negative constraint
Many XV puzzles add a negative constraint: if two adjacent cells carry no marker, their sum is not 5 and not 10. That turns every blank edge in the grid into information, and it is usually where the puzzle is actually solved. Check the puzzle's rules text — VariantDoku states explicitly whether the negative constraint applies.
VariantDoku shows the same reference inside the app: open any puzzle, tap the rules sheet, and each constraint on the grid gets its own tips card.
How to solve xv sudoku
V pairs are tiny
A V pair sums to 5, so it's one of {1,4} or {2,3} — only two options, which prunes fast.
X pairs from small clues
An X pair sums to 10: {1,9}, {2,8}, {3,7}, or {4,6}, never two 5s since digits can't repeat across the bar.
Mind the negative constraint
When the rules say all X and V are given, two neighbours with no symbol can't sum to 5 or 10 — a quiet but powerful elimination.
Memorise the six pairs
V is {1,4} or {2,3}. X is {1,9}, {2,8}, {3,7} or {4,6}. Any marked edge with one digit known resolves the other instantly.
Mine the blank edges
Where the negative constraint applies, every unmarked edge tells you two sums are impossible. Across a full row that is a large number of eliminations.
Step by step: techniques from the hint engine
Each example is drawn the way VariantDoku's hints show it: red candidates are eliminated, blue ones are what the step proves, and green cells are solved.
A pair that would starve a cell
A V can only be {1,4} or {2,3}. Another cell in this row has only 1 and 4 left, so if the V were {1,4} that cell would have no digit at all. The V must be {2,3}.
The negative constraint
Some XV puzzles promise that every X and V is shown. Then two neighbours without a mark sum to neither 5 nor 10, so next to a 3 every unmarked neighbour loses 2 (3 + 2 = 5) and 7 (3 + 7 = 10). Read the rules first: VariantDoku's XV puzzles usually say that not all marks are given, and then a blank edge tells you nothing.
A worked example
An X between two cells where one is already 3 forces the other to 7 immediately — there is no second option. A V with a known 2 forces a 3.
Under the negative constraint, a cell holding 1 tells you its unmarked neighbours are not 4 (which would make a V) and not 9 (which would make an X). Sweep that across a row of unmarked edges and the eliminations add up fast.
On 4×4 and 6×6 boards
On a 6×6 board an X can only be {4,6}, so every X locks a 4 and a 6 into its two cells and removes both digits from the rest of their row, column or box. On a 4×4 board an X is impossible — 4 + 3 = 7 is the largest sum — so 4×4 puzzles use only V's, and in a 4×4 row, column or box containing a V the other two cells also add up to 5.
| Board | V (5) | X (10) |
|---|---|---|
| 4×4 | {1,4} {2,3} | none |
| 6×6 | {1,4} {2,3} | {4,6} |
Try one from the catalog
Real VariantDoku puzzles with this rule. Each one opens in the app.
Frequently asked questions
What do X and V mean in XV sudoku?
X marks two cells that sum to 10; V marks two cells that sum to 5, from the Roman numerals X=10 and V=5.
What pairs make a V in XV sudoku?
Pairs summing to 5: {1,4} and {2,3}.
Does XV sudoku have a negative constraint?
Often yes — if the puzzle states all marks are given, an unmarked adjacent pair sums to neither 5 nor 10.
Why can't 5 appear in an X or V pair?
A V would need 5+0 and an X would need 5+5 — the first has no 0, the second repeats a digit in adjacent cells.
What is the negative constraint in XV sudoku?
When it applies, any two adjacent cells without a marker must not sum to 5 or 10. Always check the puzzle's stated rules, as not every XV grid uses it.
Play XV Sudoku in VariantDoku
VariantDoku has a logic-checked catalog of XV Sudoku and dozens of other variants on 4×4, 6×6 and 9×9 boards, with new 4×4 and 6×6 dailies every day. Free on iPhone, iPad and Android — no ads, no trackers.