Tile Flip versus Corner Flip
The same 5×5 grid, the same goal, two completely different puzzles. The single rule change that makes them different, and how to recognise it.
Two of the games in Issue One — Tile Flip (#16) and Corner Flip (#21) — look almost identical and play almost completely differently. This article is a comparative walkthrough: if you have played one and want to understand the other, or have played both and want to understand what changed, this is the side-by-side.
The shared surface
Both games present a 5×5 grid of tiles. Some are lit, some are dark. You click tiles to toggle them. Your job is to turn the entire board dark. The grids look the same, the goal is the same, the input is the same. The difference is what happens when you click.
In Tile Flip, clicking a tile toggles that tile and its four edge-neighbours (up, down, left, right). This is the classic Lights Out rule, invented in 1995.
In Corner Flip, clicking a tile toggles only its four diagonal corner-neighbours. The clicked tile itself does not change. The edge-neighbours do not change.
That single rule change produces two genuinely different puzzles.
What changes in Tile Flip's case
The Tile Flip move (centre + edges) is a connected operation: the toggled cells form a plus sign. This means moves can affect tiles in any row and any column, which gives the game a coupled, holistic feel. Solving one row almost always disturbs the next; the standard technique is "chase the lights" — solve the top row, then use the second row to fix what the first row's solution left behind, and so on.
The mathematical structure of Tile Flip is well-studied: every board is either solvable or unsolvable, and solvability depends on a parity condition involving the entire board state. The procedural mechanics — chase the lights — handle solvability cases without requiring the player to understand the math.
What changes in Corner Flip's case
The Corner Flip move (only diagonal corners) is a disconnected operation in a specific way: diagonal moves always land on a tile of the same "chessboard colour" as the original. If you imagine the 5×5 grid with cells alternately painted black and white like a chessboard, the 13 "white" cells and the 12 "black" cells never interact through diagonal moves.
This means Corner Flip is not one puzzle — it is two completely independent puzzles, one on the white cells and one on the black cells. A player who recognises this can solve each sub-puzzle in isolation, which is much easier than solving the apparent 25-tile combined puzzle.
The math here is also well-defined but quite different from Tile Flip's. The two independent sub-puzzles have their own parity conditions; solvability depends on both sub-puzzles being individually solvable.
How to recognise the difference while playing
The fastest way to feel the difference is to play one level of each back-to-back. In Tile Flip, the strategy is procedural: you follow the chase-the-lights sweep and trust the technique. In Corner Flip, the strategy is decompositional: you mentally separate the board into two chessboard-coloured layers and solve them as two separate problems.
A player who is used to Tile Flip and tries to use Tile Flip technique on Corner Flip will get worse than random results, because the diagonal move structure makes "chase the lights" actively harmful — it produces moves that cycle the same cells without progress. Conversely, a player who recognises the chessboard split in Corner Flip and tries to apply it to Tile Flip will be confused, because the edge-move structure means white and black cells do interact and cannot be solved separately.
Why both earned slots
The reason we included both games is exactly this comparison. Two puzzles that look identical and play differently are a more interesting pair than two puzzles that are visibly different. They make the underlying mathematical structure visible to a player who would never otherwise encounter linear algebra — and that visibility is what we mean when we say a game can teach something.
If you play one, we recommend Tile Flip — it scores 3.9 to Corner Flip's 3.7, and the "chase the lights" technique is more universally satisfying. If you play both, play them back-to-back; the comparison is the whole point.
Published · 14 May 2026 · Written and signed by Bill