Step 4 of 8
"3" on an edge, "2" in a corner
On the edge of the board, small numbers are just as decided as a "4".
The rule of thumb: A "3" on the edge with three open neighbors, or a "2" in a corner with two, has no choice — fill them all.
Pillars on the edge have fewer neighbors, and fewer neighbors means fewer choices. A "3" sitting on an edge (not in a corner) has exactly three white neighbors — all three hold torches. A "2" tucked into a corner has exactly two — both hold torches.
Learn the shapes the way you learned the "0": as reflexes, not arithmetic. They’re the hungry-pillar count from step 8 in its most common shapes, already done for you. The play page’s boards don’t deal "3"s, so the corner "2" is the one you’ll meet there, and it’s the one these practice boards use; take the shape away and the other rules stall.
Where to look: Edge pillars first, corners second, on every new board. Three open neighbors under a "3" on an edge, two under a "2" in a corner: fill them all.
Worked example
A real position from a board that needs "3" on an edge, "2" in a corner. Purple: what the reasoning rests on. Dashed: the cells in question. Green: what it proves.
The pillars that decide themselves are done. Next: what a placed torch forbids. Step 5: Torches can't see each other →