How to solve Girandola Sudoku
Girandola Sudoku is ordinary Sudoku with one extra unit: nine shaded cells made up of the four corners of the grid, the centre, and the four cells just inside the middle of each edge. The corners pair up along the edges and three cells line up along the middle row and column, so a single digit can rule out several of them at once.
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The rules
Fill the grid so that every row, every column and every 3×3 box holds the digits 1 to 9 once each.
In Girandola Sudoku, the nine shaded cells also hold 1 to 9 once: the four corners of the grid, the centre, and the cells in row 2 and row 8 of column 5 and in column 2 and column 8 of row 5. Each box has exactly one.
Girandola Sudoku strategies
These seven techniques put the Girandola cells to work. Everything in How to solve Sudoku still applies, with the Girandola counted as one more unit. Take care with unique rectangles: a rectangle is only a deadly pattern if the Girandola holds none of its corners, or two side by side in the same row or column.
A few terms first. The Girandola is nine cells: the four corners of the grid, the centre, and the four cells just inside the middle of each edge. In grid terms that's row 1 and row 9 in columns 1 and 9; row 2, column 5; row 5, columns 2, 5 and 8; and row 8, column 5. Each box has exactly one, in the outer corner of the four corner boxes and in the centre of the other five, so a digit in the Girandola cell of one box can't be in the Girandola cell of any other. The corners pair up along the four edges, and row 5 and column 5 each hold three Girandola cells. In the diagrams the Girandola cells are shaded grey with a small ring.
The diagrams use the same colours as our other guides. Green marks the cell the step is about and the answer it gives you. Blue marks the cells it depends on. Purple marks the cells you're scanning. Red with a cross is a candidate you can remove.
Remember to check the Girandola as you would any other unit.
Singles in the Girandola
Count the Girandola too
Seeing it. No two Girandola cells share a box, so each one has neighbours the ordinary rules don't give it. A Girandola cell is often down to one candidate sooner than you'd expect. In the diagram, the green cell is row 9, column 9, the bottom right corner of the grid. Its row, column and box hold every digit except 7 and 8.
Using it. Now look at the other Girandola cells. Row 2, column 5 is already 7, so the green cell can't be 7 and must be 8. When you list the candidates for a Girandola cell, always check the digits in the other eight.
The Girandola, rows and columns
The Girandola along a row or column
Seeing it. This works like a pointing pair. Look for a digit whose only places in the Girandola are on one row or one column. The two corners on each edge are the likely ones. In the diagram, the Girandola can only take 3 in column 1: row 1 or row 9.
Using it. The Girandola's 3 is in column 1, so column 1's 3 is one of those two corners. Remove 3 from the rest of the column. Here that's the green cell, row 7, column 1, which is left with 2 or 4.
The Girandola, rows and columns
A row or column that points into the Girandola
Seeing it. Now turn it round. Look for a row or column whose only places for a digit are Girandola cells. In the diagram, column 9 can only take 5 in row 1 or row 9, and both are corners.
Using it. Column 9's 5 is in a Girandola cell, so the Girandola's 5 is in column 9, and no Girandola cell outside column 9 can be 5. The green cell, row 1, column 1, loses its 5 and is left with 2 or 9.
Pairs in the Girandola
Pairs in the Girandola
Seeing it. A naked pair works across the Girandola the way it does in a box. In the diagram, row 5, column 2 and row 9, column 1 can only be 1 or 6. They share no row, column or box, so only the Girandola links them.
Using it. Those two cells take the Girandola's 1 and 6 between them, so no other Girandola cell can be 1 or 6. The green cell, row 5, column 8, loses its 1 and is left with 2 or 5.
Cells that see two places
Two places seen from the Girandola
Seeing it. Look for a digit with exactly two places in a row, column or box, then for a cell that sees both of them. The Girandola lets a cell see a place it would never reach through its row, column or box. In the diagram, column 5 can only take 7 in row 1 or row 8, and row 8, column 5 is a Girandola cell.
Using it. One of those two cells is 7. The green cell, row 1, column 1, is in row 1 with the first and in the Girandola with the second, so whichever holds the 7, the green cell sees it. It can't be 7 and is left with 5.
