Pick the digit that appears most
Count the givens. A digit that already appears five or six times has only three or four copies left to place, and the existing copies block most of the grid for it.
The grid on the right is the starting position of a real daily puzzle. It has six 5s and five 7s, so those are the digits to try first. A digit that appears once or twice can wait.
Cross-hatch one box at a time
Take the digit 5 and look at box 1, in the top-left corner. It has no 5 yet and four empty cells.
Now look along the lines that pass through the box. Row 2 already has a 5, over in column 7, so neither empty cell in the middle row of the box can be 5. Column 1 has a 5 at the bottom, in row 9, so the empty cell at the top of that column is out too.
One empty cell is left: row 1, column 3. The 5 goes there. This is a hidden single, and scanning is the quickest way to find one.
Use every line that crosses the box
Sometimes two lines aren’t enough and a third finishes the job. Take the digit 7 and box 2, at the top of the middle stack. The box has six empty cells.
The 7 in row 1 rules out the two empty cells in the top row of the box. The 7 at the end of row 2 rules out the two in the middle row. That leaves two cells in the bottom row, and the 7 in column 4 removes one of them. The 7 goes in row 3, column 5.
Work through the boxes in a fixed order, for example along each band from left to right. A fixed order stops you from checking the same box twice and missing another.
Then check the fullest rows, columns and boxes
When a pass through the digits finds nothing new, change the question. Look for the unit with the fewest empty cells and ask which digits it is missing.
In the opening position, row 2 has five givens and the top-left box has five. The cell where they meet, row 2, column 3, can see eight different digits between its row, column and box. Only 9 is missing, so the cell is a 9. That is a naked single, and the naked singles page shows this very cell.
A unit with one empty cell is the easiest case of all. Solvers call it a full house: write in the missing digit.
Go round again
Every digit you place is a new blocker. After a placement, scan that digit again, and check the row, column and box you just added to. Placements tend to come in runs.
This daily puzzle can be finished with singles alone, and so can most puzzles rated easy or medium. When a full pass through digits 1 to 9 and a check of the fullest units both come up empty, it is time to write notes and look for pairs.
- Scan the most common digit first, box by box.
- After each placement, scan that digit again.
- When scanning stalls, check the fullest rows, columns and boxes.
- Only then start writing notes.