The goal is to fill the 9x9 grid with digits from 1 to 9 based on three absolute rules:
The rules are identical to Classic, but instead of 3x3 square blocks, the 9-cell regions have irregular jigsaw-like shapes marked by thick borders.
Scan the grid for any row, column, or block that has 8 out of 9 cells filled. By simple elimination, the remaining empty cell must contain the only missing digit from 1 to 9.
Look at a specific empty cell. If the row, column, and 3x3 block intersecting that cell already contain 8 different numbers (e.g., 1,2,3,4,6,7,8,9), the only physically possible candidate left for that cell is a 3.
Focus on a 3x3 block and track a specific number. If you realize that the number 5 cannot be placed in any other empty cell in that block (because those cells are blocked by 5s in other rows/cols), you must place it in the one remaining valid cell.
If two empty cells in the same row, column, or block contain EXACTLY the same two note candidates (e.g., only 6 and 9), no other cell in that house can contain 6 or 9. You can safely erase 6 and 9 from all other notes in that row/block.
If two specific numbers (like 2 and 6) appear as notes in ONLY two cells within a block, they must belong in those two cells. Therefore, you can erase all other candidate notes from those two specific cells.
If the note for a certain digit within a 3x3 block appears only in one single row or column, the solution for that block MUST be in that line. Consequently, you can erase that digit from the rest of that row/column outside the block.
Find a specific digit that appears as a note in exactly TWO cells of a row, and repeats this pattern in another row, perfectly aligned in the same two columns (forming a rectangle). Because the digit must be placed diagonally across those corners, you can eliminate that digit from all other cells in those two columns.
Look for a 'hinge' cell with exactly 2 candidates (e.g., A,B) and two 'wing' cells (A,C and B,C). If the hinge is A, the first wing must be C. If the hinge is B, the second wing must be C. Therefore, any cell intersected by BOTH wings can NEVER contain candidate C.
The Swordfish is a 3x3 extension of the X-Wing. If a digit is limited to 2 or 3 cells across three different rows, and those cells align perfectly within exactly three columns, you can eliminate that candidate from all other cells in those three columns.