All Sudoku Variants
9×9 · Arithmetic

XV Sudoku

Marks between cells give sums: an X means the two digits add to 10, a V means they add to 5.

6 4 2 3 9 8XV

An example XV puzzle: an X marks two cells summing to 10 (6, 4); a V marks two summing to 5 (2, 3).

XV Sudoku borrows two letters from Roman numerals and turns them into clues. Between some pairs of touching cells you will find an X or a V: since X is the Roman ten and V the Roman five, an X means the two digits add up to 10 and a V means they add up to 5. Read carefully, these little marks — and the gaps where they are missing — solve the whole grid.

The two marks and what they mean

  • An X between two cells means their digits sum to 10 — pairs like 6 and 4, or 3 and 7.
  • A V means the digits sum to 5 — pairs like 1 and 4, or 2 and 3.
6 4 3 7 1 4 2 3XXVV

An X marks a sum of 10 (6+4, 3+7); a V marks a sum of 5 (1+4, 2+3).

Reading a single mark

Each mark is a candidate filter you can apply on sight. An X allows only the pairs that make 10 with two different digits: 1–9, 2–8, 3–7 and 4–6. Note that 5 cannot sit on an X inside a single unit, because its only partner for 10 would be another 5. A V is even more restrictive: the only pairs summing to 5 are 1–4 and 2–3, so a cell touching a V can only ever be 1, 2, 3 or 4 — the digits 5 through 9 never appear beside a V.

The negative constraint

In the standard "full" version, every X and V that could be drawn is drawn. That makes the blank edges speak too: if two adjacent cells carry no mark, then their digits do not sum to 5 and do not sum to 10. A bare edge next to a 6, for instance, forbids a 4 (that would be an X) and forbids nothing for 5 — a quiet but constant source of eliminations that cracks the harder puzzles.

Forced neighbours at the extremes

As in most marked-pair variants, the edges of the number range collapse to a single option. A 9 can only make 10 with a 1, so an X on a 9 forces its neighbour to 1 — and a 9 can never touch a V at all, since nothing pairs with 9 to make 5. The same tightness appears wherever a large digit meets a mark.

9 1 4 1 8 2XVX

A single mark can force the neighbour: 9X needs 1, 4V needs 1, 8X needs 2. Green cells are forced.

A worked example, step by step

Watch a V and an X chain together. Three cells sit in a row: the first is a given 3, joined to the second by a V, and the second to the third by an X.

3VX

Step 0. A given 3, a V, then an X.

Step 1 — read the V. A V means the first two cells sum to 5. With the first cell a 3, the second must be 5 − 3 = 2.

3 2VX

Step 1. V (sum 5) with a 3 forces the middle cell to 2.

Step 2 — read the X. An X means the second and third cells sum to 10. The second is now 2, so the third must be 10 − 2 = 8. Two marks and one given have solved the whole row: 3-2-8.

3 2 8VX

Step 2. X (sum 10) with a 2 forces the third cell to 8 — the row reads 3-2-8.

Solving strategy

  • Start on the V marks. They confine both cells to {1, 2, 3, 4}, the tightest clue on the board.
  • Chase the big digits. An X on an 8 or 9 usually forces its partner outright.
  • Use the missing marks. In full XV, a bare edge rules out the 5-sum and 10-sum partners — do not leave that information on the table.
  • Feed the grid. Each forced digit behaves like a given for its row, column and box; chase the singles it creates.

Common mistakes

  • Confusing the letters. X is ten, V is five — mixing them inverts every deduction.
  • Reading a mark as an order. A mark never says which cell is larger; 6–4 and 4–6 both satisfy an X.
  • Putting 5–9 on a V. Only 1, 2, 3 and 4 can sit beside a V — anything higher is impossible.
  • Ignoring the blank edges. In the full version, the absence of a mark is as strong a clue as its presence.

Can I play it here?

Not yet — XV Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: