Play this puzzle before you read on. It is the expert daily from Sunday 27 September, rebuilt from its date, so it is the same grid that was on the leaderboard that day.
The starting grid
Daily #19 as served: 25 clues, 56 empty cells.
Twenty-five clues is low even for an expert grid, and they are unevenly spread: row 1 has two, row 4 has two, and the bottom-left box has just an 8 and a 3. That is the first thing to read in a grid like this. Sparse areas will not give anything away by counting cells, so the opening has to come from digits rather than cells.
The opening: look for digits, not cells
The first six moves are all hidden singles. The 8 in row 1 can only go in R1C6, the 1 in column 1 can only go in R9C1, the 2 in row 2 only in R2C7, and so on. Not one empty cell at the start has a single candidate, so a solver who scans cell by cell finds nothing. A solver who takes each digit in turn and asks where it can go in each row finds a move straight away.
Once those six are in, the grid opens up. From move 7 onwards most of the work is naked singles, with a few more hidden singles in between. By move 37 there are 19 empty cells left and nothing single remains anywhere.
Move 38: the XY-Wing
Move 38 of 56. R5C1 holds 3 or 9; either way R4C3 or R5C6 must be 6, so 6 goes from every cell both of them see. Then R4C6 = 4 follows. Blue: the pivot and both pincers. Red: the cell that loses its 6.
Here is the position with candidates. R5C1 can only be 3 or 9. In its own box, R4C3 can only be 6 or 9. Along row 5, R5C6 can only be 3 or 6. That is the XY-Wing shape: a two-candidate pivot, and two two-candidate pincers that each share one digit with it and share a third digit, 6, with each other.
Follow both cases. If R5C1 is 9, then R4C3 cannot be 9, so it is 6. If R5C1 is 3, then R5C6 cannot be 3, so it is 6. One of the two pincers is a 6 whatever the pivot turns out to be. So any cell that sees both pincers cannot be 6, and R4C6 sees R4C3 along row 4 and R5C6 inside box 5.
R4C6 had two candidates, 4 and 6. Without the 6 it is a 4, and that one placement is all the grid was waiting for. Every one of the remaining eighteen moves is a naked single.
How you could have found it
- When singles run out on an expert grid, list the cells with exactly two candidates. There were only a handful here, and three of them made the wing.
- For each two-candidate cell, look for two others it can see that each share one of its digits. If those two have the same second digit, you have a wing.
- Then check which cells see both pincers. Here there was exactly one, which is common: an XY-Wing usually removes one or two candidates, not ten.
The whole path at a glance
| Technique | Moves |
|---|---|
| Naked single | 44 |
| Hidden single | 11 |
| XY-Wing | 1 |
| Total moves | 56 |
Fifty-five of the fifty-six moves are singles, so this puzzle was graded expert for two reasons: a long path through a sparse grid, and one move that needs a pattern spanning a box and a row. That is typical. Across the 300 expert grids we measured, only about one in twelve needs a wing or a fish at all; the rest are expert because of how much they ask of you, not because of one exotic move. Read more about the pattern in the XY-Wing guide.