XV Sudoku: Rules and Solving Strategy

Read V and X clues as fixed sums

XV Sudoku keeps the standard requirement that every row, column, and 3 by 3 box contains the digits 1 through 9 once. A V placed between two orthogonally adjacent cells means those digits add to 5. The possible unordered pairs are 1 and 4 or 2 and 3. An X means the neighboring digits add to 10, giving the pairs 1 and 9, 2 and 8, 3 and 7, or 4 and 6. The digit 5 cannot participate in a V pair with another legal positive digit, and it would require another 5 for an X pair, which ordinary Sudoku peers cannot allow. The clue does not specify which side holds the larger digit. Rows, columns, boxes, and other XV clues decide the order. Shapedoku uses symbols without numerical sums, so these Roman numeral clues are not part of its classic boards, but the same disciplined candidate work remains essential.

Confirm whether missing clues are negative

Some XV puzzles use a negative constraint. In that form, any adjacent pair without a V or X must not sum to 5 or 10. Other puzzles display only selected clues, so an unmarked pair may still have either total. The instructions must state which convention is active. Under a full negative rule, a placed 1 removes 4 and 9 from every unmarked orthogonal neighbor, while a placed 2 removes 3 and 8. Those are powerful eliminations, but they are completely invalid in a partial-clue puzzle. Read the rules before building candidates. Also remember that diagonal cells are not XV neighbors unless another rule connects them. A clue belongs only to the two cells it separates. When symbols are crowded around a box border, trace the small mark carefully so you do not attach it to the wrong pair, a surprisingly efficient way for a tidy grid to become nonsense.

Use linked sums to force digits and pairs

An XV clue immediately creates a small candidate set. If one side of a V can only be 1 or 2, the other side must be 4 or 3 respectively. Candidate changes should always be copied across the clue. Chains of clues are stronger. Suppose three cells form V then X. If the first cell is 1, the middle must be 4, and the third must be 6. If the first is 2, the middle must be 3, and the third must be 7. Crossing units may remove one entire sequence. Boxes can also lock pair digits. A V pair inside one box must use either 1 and 4 or 2 and 3, so placed digits elsewhere in the box may settle the combination before the exact order is known. Treat each clue as a two-cell equation, then return to classic Sudoku logic. One resolved sum often creates a hidden single in a row or a naked pair in the surrounding box.

1. Mark V pairs as 1 and 4 or 2 and 3.
2. Mark X pairs as 1 and 9, 2 and 8, 3 and 7, or 4 and 6.
3. Check whether unmarked neighbors carry a negative constraint.
4. Intersect each sum pair with the candidates allowed by its two cells.
5. Propagate every candidate removal across the clue.
6. Use rows, columns, and boxes to determine the order of each surviving pair.