XV Sudoku

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.

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.

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.

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.

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.

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:

• Try the closely related Killer, which you can play right now.
• Browse all the Sudoku variants we do offer.
• Or print free puzzles from the printable PDF page.

Where to play it

XV Sudoku belongs to the arithmetic family and runs on 9×9. It is not one SudokuStreak generates yet - but the deduction it trains is the deduction every Sudoku runs on.

Difficulty and type are two separate dials here: the type sets the extra rule, the level sets how much of the grid you start with. Easy Sudoku leaves 36 of the 81 cells filled, so there is always an obvious next move somewhere; Hard Sudoku leaves 26, where scanning gets you started and then leaves you stranded. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.

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