Argyle Sudoku: Rules and Solving Strategy

Argyle Sudoku adds no-repeat rules on marked diagonals

Argyle Sudoku begins with normal classic Sudoku: each row, column, and 3x3 box contains 1 through 9 exactly once. The extra information comes from a set of marked diagonal lines that cross the grid in an argyle-like pattern. A digit may not repeat on any one marked diagonal. Unlike Diagonal Sudoku, where the two long corner-to-corner diagonals normally form complete nine-cell units, Argyle Sudoku can use several shorter marked diagonals. A line does not necessarily contain all nine digits, so think of it as a no-repeat group rather than a complete 1 through 9 set. That distinction matters. If a marked diagonal contains five cells, you may eliminate a placed 6 from the other four cells on that line, but you cannot conclude that the line must eventually contain 1, 2, 3, 4, and 5 or any other predetermined set. Before solving, trace each diagonal from end to end so you know which cells share it. At crossings, a single cell may be constrained by two marked diagonals in addition to its row, column, and box.

Let diagonal pressure shrink ordinary candidates

The best Argyle Sudoku deductions often start with an ordinary candidate list and become decisive only after diagonal exclusions are added. Suppose a cell can be 2, 5, or 8 from its row, column, and box. If a 2 already appears on one marked diagonal through that cell and an 8 appears on the other, the cell is forced to 5. This local pressure can cascade. A solved crossing cell removes its value from two diagonal groups at once, which may narrow other cells in different boxes. You can also use subset logic when several cells on the same diagonal share a small candidate set, but remember that the line is only a no-repeat group. A pair of cells restricted to 3 and 7 means those values are reserved within that diagonal segment, so other cells on the same marked line cannot use 3 or 7. The same candidates may still appear elsewhere in the row or box if standard rules permit. In Shapedoku, this is similar to following one glowing symbol through several overlapping visual groups: the symbol has no arithmetic role, only a uniqueness constraint wherever the rules say the cells are linked.

Solve Argyle Sudoku by tracing lines deliberately

Argyle Sudoku becomes confusing when you rely on memory for which cells share a marked line. Use a deliberate scan. Pick one diagonal, follow it from one end to the other, and update candidates for every solved digit on it. Then move to the next line. After a diagonal pass, return to classic Sudoku because the strongest consequence may be a normal hidden single or locked candidate. Crossings deserve special attention: if a cell lies on two marked diagonals, a placement there sends two extra waves of eliminations across the grid. Also distinguish a visual crossing from a logical connection. Two diagonal lines may cross inside the same cell, which clearly links through that cell, but separate nearby lines are not related unless the printed pattern says they are the same marked diagonal. On paper, light candidate notation helps. In an app, complete Notes reduce the risk of leaving stale candidates after a diagonal placement. The goal is not to hunt exotic patterns first. Use the extra no-repeat lines to make the familiar row, column, and box logic stronger.

1. Trace every marked diagonal before making advanced deductions.
2. Remove a placed digit from every other cell on the same marked line.
3. Remember that short diagonals are no-repeat groups, not automatically complete 1 through 9 units.
4. Prioritize cells where two marked diagonals cross because they receive the most extra pressure.
5. After each diagonal elimination, rescan the affected row, column, and box.
6. Use subsets on a marked line only when the candidate confinement is logically complete.