Play this puzzle first. It is the hard daily from Saturday 12 September, rebuilt from its date.
The starting grid
Daily #4 as served: 30 clues, 51 empty cells.
Thirty clues is generous for a hard grid, and column 3 in particular is nearly empty while the rows through it are well filled. That combination is a gift: every empty cell in column 3 is seen by a lot of placed digits.
The opening: column 3 falls first
The first six moves are naked singles, and every one of them is in column 3: R3C3 = 9, R1C3 = 1, R6C3 = 2, R4C3 = 4, R5C3 = 3, R9C3 = 8. Each cell there sees eight different digits along its row, its column and its box. Three hidden singles follow, the first of them the 3 in R7C1.
After nine moves there are 42 empty cells and no single anywhere. This is the wall the hard page describes, and it comes early.
Move 10: box/line reduction
Move 10 of 50. In column 2, 1 only fits inside box 7, so it can be removed from the rest of that box. With that settled, R5C2 = 7, R7C2 = 2 follow. Blue: the only cells in column 2 that can still hold a 1. Red: the cells in box 7 that lose it.
Look down column 2 for the digit 1. Most of the column is already filled, and of the empty cells only R8C2 and R9C2 can take a 1. Both of them are in box 7, the bottom-left box. Column 2 has to have a 1 somewhere, so it must be in one of those two cells, which means box 7's 1 is in column 2.
So the 1 cannot be anywhere else in box 7. R8C1 and R9C1 both had 1 as a candidate, and both lose it. That reduces them to 7 and 9 each, and from there the next placements come quickly.
This is the box/line direction of locked candidates: a line confines a digit to one box, so the box loses it elsewhere. The other direction, the pointing pair, runs the opposite way. The solver lists this move twice in a row, because the same locked 1 is what it leans on again before the next placement.
How you could have found it
- When singles stop, go digit by digit through the nearly full lines. A line with only two or three cells left for a digit is where locked candidates live.
- Check whether those cells share a box. If they do, the rest of that box is clear of the digit.
- This is cheaper than writing out every candidate, and on hard grids it is usually enough.
The whole path at a glance
| Technique | Moves |
|---|---|
| Naked single | 43 |
| Hidden single | 5 |
| Box/line reduction | 2 |
| Total moves | 50 |
Forty-eight of the fifty moves are singles. About one hard grid in five needs a locked-candidate move like this one, and the rest are hard because hidden singles carry them throughout. The pointing pairs guide covers both directions with another worked example.