A square diagonal to a number shares a row with one of the number’s squares and a column with another. A bulb there would light both, so neither could take a bulb. If that leaves the number short of room, the diagonal gets no bulb.
This is one of the Light Up techniques. Each page shows its technique on the same 12×12 from the game, Hard level 4.
The rule
- Find a number that still needs bulbs, and count its open squares.
- Look at a square diagonal to it that sees two of those open squares.
- If the open squares minus those two are fewer than the bulbs it still needs, put a dot on the diagonal.
The classic case is a 3 in the open: it needs three of its four squares, and a bulb on any diagonal would leave only two. So all four diagonals get dots.
In a real puzzle
On the 12×12, it’s first needed at step 25. The 1 in row 4, column 2 still needs its bulb, and only two squares are left for it: the one below it and the one to its left. A bulb in row 5, column 1, diagonal to the 1, would light both. So no bulb goes there.
How often you’ll need it
On 19 of the 50 Easy levels, 27 Medium and 49 Hard: 0.9 times per Easy level on average, 1.5 on Medium and 6.6 on Hard. It’s 1 of the 42 steps on the 12×12 here.