XV Sudoku: rules, tips and free puzzles

XV sudoku borrows two Roman numerals. An X between two cells means they add up to 10; a V means they add up to 5. Every X and V in the grid is drawn, so their absence tells you something too.

It is a lovely variant for practising sums and negative clues together, and it plays very differently from killer despite the arithmetic.

The rules

• Normal sudoku rules apply: 1 to 9 once in every row, column and 3×3 box.
• An X between two cells: their digits sum to 10.
• A V between two cells: their digits sum to 5.
• Every possible X and V is shown. Neighbours with no symbol never sum to 10 or 5.

How to start

Learn the pairs

X pairs are 1+9, 2+8, 3+7 and 4+6. A 5 can never sit on an X, because 5 + 5 would repeat a digit in a row or column. V pairs are just 1+4 and 2+3, so any cell touching a V is 1, 2, 3 or 4.

Use parity

An X joins two odds (1+9, 3+7) or two evens (2+8, 4+6). A V always joins one odd and one even. If you know a cell’s parity, you know its partner’s.

Use the absences

A 9 with no X beside it means none of its neighbours is a 1. A 2 with no V means none of its neighbours is a 3. On a sparse XV grid, these quiet clues usually break the deadlock.

Common mistakes

• Putting a 5 on an X. It would need another 5 right beside it.
• Forgetting that missing symbols are information.
• Mixing up X and V. X is 10, V is 5.

How the ranks scale difficulty

Every puzzle type on Hoot’s Puzzles comes in four ranks, named after the stages of a mathematical idea. Lemma is the warm-up: about a dozen more digits are given than logic strictly needs, and singles plus the variant’s own rule will carry you through. Proposition needs a real idea or two, typically pointing and claiming. Theorem is near-minimal, so almost every clue is load-bearing and you may need pairs. Conjecture gives the fewest digits and sparser rule clues: expect to think hard.

All the Xs and Vs are drawn at every rank, because the negative clues depend on it. Rank changes how many digits you start with and how much logic you need to string together.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• Kropki SudokuWhite dots for consecutive pairs, black for a 1:2 ratio. Missing dots matter.
• Killer SudokuCages with sums instead of given digits. Partition arithmetic and the rule of 45.
• Non-Consecutive SudokuSide-by-side cells never hold consecutive digits.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.