An example Modular Lines puzzle: every three cells in a row hold three different remainders mod 3 - one each from {1,4,7}, {2,5,8}, {3,6,9}.
Modular Lines Sudoku groups the digits by their remainder when divided by 3: {1, 4, 7}, {2, 5, 8} and {3, 6, 9}. Along a modular line the rule is that any three cells in a row must come from three different groups - one from each remainder class. It is the modular cousin of the entropic line, which groups by size instead of by remainder.
The rule: one remainder each, every three cells
Take any run of three consecutive cells on the line: it must hold one digit from {1,4,7}, one from {2,5,8} and one from {3,6,9}. Below, the colours mark the three remainder groups, and every three-in-a-row (1-2-3, 2-3-4, 3-4-5) has one of each.
{1,4,7}, {2,5,8}, {3,6,9}: every three-in-a-row has one from each group.
A worked example, step by step
Take a line whose first two cells are a 1 and a 2, third cell empty.
Step 0. First two cells: 1 (group {1,4,7}) and 2 (group {2,5,8}).
Step 1 - identify the groups used. The 1 belongs to {1,4,7} and the 2 to {2,5,8}. Those are two of the three remainder groups, so the first three cells have already used them.
Step 2 - the third takes the last group. Only {3,6,9} is left, so the third cell must be a 3, 6 or 9.
Step 2. Two groups are used, so the third cell is from {3,6,9}.
The cycle repeats
As with entropic lines, the three remainder groups march in a fixed cycle along the whole line: once two neighbouring cells are grouped, every other cell's group is decided. That turns even a scattered pair of clues into a constraint on the entire line, which is why modular lines resolve so much of a grid at once.
Solving strategy
- Group before you place. Work out the {1,4,7}/{2,5,8}/{3,6,9} pattern along the line first.
- Two cells fix the cycle. Any two adjacent groups pin the rest of the line.
- Then use the grid. A cell narrowed to one group of three is easy for the rows, columns and boxes to finish.
- Feed the grid. Each digit fixed on the line behaves like a given for its row, column and box.
Common mistakes
- Checking only the first three. Every consecutive three must span all three groups, not just the opening trio.
- Grouping by size. Modular lines group by remainder (1-4-7 together), not by low/middle/high - that is the entropic line.
- Reading a group as one digit. {3,6,9} still needs the ordinary rules to pick the exact value.
- Forgetting ordinary Sudoku. Line cells still can't repeat within a row, column or box.
Can I play it here?
Not yet - Modular Lines 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:
- Browse all the Sudoku variants we do offer.
- Or print free puzzles from the printable PDF page.
Where to play it
Modular Lines Sudoku belongs to the constraint 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. Expert Sudoku leaves 25 of the 81 cells filled, where the beginner tools dry up almost entirely; Evil Sudoku leaves 23, with no easy moves at all. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.