Quadruple Sudoku: Rules and Solving Strategy

Read each clue as a four-cell requirement

Quadruple Sudoku keeps the classic rule that every row, column, and 3 by 3 box contains 1 through 9 exactly once. At selected intersections, a small circle lists one to four digits. Every listed digit must appear in one of the four cells touching that intersection. If a clue shows 2, 5, and 8, those three digits occupy three of the four surrounding cells, while the fourth cell contains another value. A clue listing four digits fixes the complete set for the four cells, though not their order. A repeated digit is usually not listed twice because the surrounding cells often share rows, columns, or boxes that prevent duplication, but always follow the puzzle's stated convention. Shapedoku itself does not use Quadruple clues. Its classic box scanning is still useful because these intersections often sit across box borders and require careful tracking of which four cells belong to the clue.

Place clue digits by crossing restrictions

Begin by writing each clue digit into the candidate lists of all surrounding cells where it is legal. Then use rows, columns, and boxes to reduce those positions. Suppose a clue requires a 7, but three of its four cells see existing 7s through their units. The fourth cell must be 7. If a clue requires 2 and 6 and only two surrounding cells can contain either value, those cells reserve 2 and 6 as a pair even when the order remains unknown. Clues can also eliminate candidates that are not listed. When a four-digit clue fully specifies its surrounding set, every other digit can be removed from those four cells. A three-digit clue does not permit the same broad elimination because the fourth cell remains unrestricted except by normal Sudoku logic. Keep the distinction clear: listed digits are guaranteed to appear, but unlisted digits are forbidden only when all four positions are already accounted for.

Use overlapping clues to transfer information

Neighboring Quadruple clues may share one or two cells. Compare their required sets rather than solving each clue alone. If one clue requires 1, 4, 7, and 9 while an overlapping clue requires 1, 4, and 7, the shared cells may be forced to carry part of the common set, leaving 9 in a nonshared cell of the first clue. Exact conclusions depend on which digits can reach each cell, so draw the overlap carefully. A placed digit should be removed from every other position in all clues it touches, just as it is removed from its row, column, and box. On harder puzzles, a clue may create a hidden pair across cells that do not look related under classic Sudoku alone. Full Notes help reveal those small sets. After resolving one clue digit, rescan the surrounding boxes because a placement at an intersection can affect two rows, two columns, and up to four local clue groups at once.

1. Identify the exact four cells surrounding each clue circle.
2. Add every listed digit only to surrounding cells where it is legal.
3. Place a clue digit when only one of the four cells can contain it.
4. Use two remaining positions as a pair when they hold two required digits.
5. Compare overlapping clues and separate shared from nonshared cells.
6. Update every touching clue after each confirmed placement.