Windoku – Hard

Solving Windoku: Rules and Strategies

Windoku is a Sudoku variant. Four additional 3×3 areas are offset between the normal Sudoku blocks.

Windoku is also known as Hyper Sudoku or Four-Box Sudoku.

Each marked window contains the numbers 1 to 9 exactly once.

The goal is a completely and correctly filled puzzle. Each entry must be derived from the visible clues and the already placed numbers.

Rules

• Each cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 without repetition.
• Each column contains the numbers 1 to 9 without repetition.
• Each normal 3×3 block contains the numbers 1 to 9 exactly once.
• Each marked window contains the numbers 1 to 9 exactly once.
• Pre-filled numbers are not changed.
• Each entry must satisfy all rules.

Grid Orientation

Rows are numbered from top to bottom, columns from left to right. For example, (4,7) means row 4 and column 7.

The images show specific intermediate states. Blue marked fields are used for the step, red means excluded, and green shows a confirmed result. Yellow highlights the current cell. Small numbers in an empty cell are candidates; a circle indicates the logically determined value.

Basic Idea for Solving

View each beige window like an additional 3×3 block. The strongest steps often occur where a window overlaps with a normal block, a row, or a column.

After each confirmed entry, check the affected row, column, block, and all additional hints again. Often, this reveals the next step.

1. Recognize an Additional Windoku Window

The four beige marked 3×3 areas are additional regions. They do not replace the normal blocks but are valid simultaneously.

The blue border encloses Windoku window 1. Each cell inside it belongs to its row, column, normal block, and additionally to this window.

2. Complete a Nearly Full Additional Group

In Windoku window 1, numbers 1, 2, 4, 5, 6, 7, 8, 9 are already present. Only 3 is missing; the cell (4,2) is still empty.

This means 3 belongs to (4,2). The image intentionally shows the gap still open; the circled candidate is the resulting entry.

3. Use the Additional Rule First as a Candidate Exclusion

Row, column, and normal block initially leave 1, 7, 9 possible in (2,2). However, 7 is already in Windoku window 1 at (3,4).

Therefore, 7 is eliminated. In the open cell, 1 and 9 remain. This step does not solve the cell immediately but visibly reduces its candidate list.

4. Find the Last Candidate Using the Additional Group

Without the additional rule, both 9 and 7 would still be possible in (2,2). The 7 is already used in the similar additional area at (3,4).

Thus, only 9 remains. The target cell is empty in the image and shows the circled candidate 9; the number is only entered afterward.

5. Find the Only Spot for a Number in the Additional Group

In Windoku window 1, four cells are still open for 9. Three are excluded by normal Sudoku units: (2,3) by the 9 at (7,3); (2,4) by the 9 at (3,6); (3,2) by the 9 at (3,6).

Only (2,2) remains as the place for 9. The cell itself still has candidates 1, 5, 8, 9; thus, the number is determined through its only position in the additional group.

6. Insert Two Missing Numbers in Correct Sequence

In Windoku window 1, only 9 and 7 are missing; they belong to (2,2) and (3,4). At (2,8), 7 already appears in a normal Sudoku unit with (2,2).

Therefore, 7 cannot be after (2,2) because 9 is there. For (3,4), 7 is subsequently placed. A normal unit thus determines the order of the pair.

7. Prepare a Follow-up Step with the Additional Group

In Windoku window 2, only 2 is missing at (2,6). The same row still has (2,6) and (2,9) empty.

The additional group first places 2 at (2,6). Before this entry, the row cannot distinguish between the two open cells.

8. Execute the Prepared Row Step

After entering at (2,6), only (2,9) remains empty in that row. The other eight numbers are all visible in the image.

In (2,9), 4 is missing. Here, the additional rule provides the first entry, leading immediately to a normal Sudoku step.

Typical Solving Process

1. Solve confirmed entries in rows, columns, and normal 3×3 blocks.
2. Then go through each marked additional group completely.
3. Eliminate numbers already present in the additional group.
4. Look for a missing number with only one possible place in the additional group.
5. Connect pairs and small candidate groups with the normal Sudoku units.
6. After each entry, recheck all normal and additional groups of the cell.

Common Mistakes

• Overlooking the marked additional area: A candidate allowed there can already be present.
• Comparing only neighboring marked cells: The entire additional area is a common unit.
• Confusing additional group with the normal block: Both groups are valid simultaneously and have different boundaries.
• Only searching for complete groups: A single exclusion via the additional rule can enable the next step.
• Checking only the row after an entry: The affected additional group must also be read again immediately.
• Rushing too early: If multiple numbers are possible, the cell is not yet solved.
• Not rechecking after an entry: A new number can immediately solve further cells.

Tips for Beginners

• Fully mark or track an additional group instead of just neighboring cells.
• Look for additional groups with many numbers already placed.
• Check four areas for each cell: row, column, normal block, and additional group.
• A candidate that is possible traditionally can be forbidden by the additional group.
• Use two missing numbers in an additional group together with rows or columns to establish their order.
• Scan the additional group again immediately after each entry.

Solve Windoku in small, secure steps. Recheck the affected row, column, block, and additional hints after each entry. This way, you often reach the goal without guessing.