Nine Glass Lanterns
Read the puzzle
Nine lantern tiles form a 3 by 3 grid: A, B, C on the top row, D, E, F in the middle and G, H, I on the bottom. Tiles A, D, E and G are dark; B, C, F, H and I are lit. A tap flips the tapped tile plus the tiles directly above, below, left and right of it: lit turns dark and dark turns lit. Which one tap lights all nine tiles?
Which ONE tap lights all nine tiles?
Which tile's tap covers exactly the dark tiles?
D
Tapping D flips A, D, G and E: all nine shine.
How to solve it
Step one: list the dark tiles. They are A, D, E and G. A single tap must flip all four of these and must not touch any lit tile, because a lit tile that gets flipped goes dark.
Step two: write down what each candidate tap flips. A tap on D flips D itself, A above it, G below it and E to its right. D has no tile to its left, since it sits on the edge. So D flips exactly A, D, E and G.
Step three: confirm. After the tap, those four turn lit and B, C, F, H and I were never touched, so all nine shine.
The usual wrong answer is E, the centre tile, because the middle feels like the most powerful tap. E flips five tiles: E, B, D, F and H. It lights D and E, but it also turns B, F and H dark and leaves A and G dark, so five tiles end up dark. A fails too: it flips A, B and D, darkening B and missing E and G.
Takeaway: in one-tap flipping puzzles, look for the tile whose pattern of neighbours matches the dark tiles exactly.
