Same sliding board, same 4×4 grid, different merge rule: instead of doubling, two tiles merge by adding — 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, and so on. The catch is that not every matching addition is allowed: two tiles only merge when they sit next to each other in the sequence 1, 1, 2, 3, 5, 8, 13, 21…. So 3 and 5 merge into 8 (they're neighbours in the sequence), but 3 and 8 do not, and neither do two separate 5s — 5 only pairs with the numbers next to it, 3 and 8. New tiles spawn as 1 or 2.
Why the merge rule changes the game
In classic 2048, any two matching tiles are always a valid move — the question is only whether you want to take it yet. Here, whether two tiles can merge at all depends on which specific neighbour they landed next to, which makes reading the board a step slower and planning a move ahead more valuable. Fibonacci also grows more slowly than doubling (about 1.618× per merge instead of 2×), so building a large tile takes noticeably more merges than the same-looking number would in the classic game.
The winning tile is 2584 — the point in the sequence that keeps a full run roughly as long as a classic 2048 game, given that slower growth rate. Prefer the original merge rule? Head back to the classic 4×4 game, or try the hexagonal board for a different kind of variant.