Published by Nikoli, Kojun combines the combinatorial beauty of Latin squares with a clever vertical gravity mechanic.

The Golden Rules of Kojun

• Region Sizes: A room containing \(K\) cells must contain every integer from \(1\) to \(K\) exactly once. A 1-cell room always contains a 1!
• No Neighbor Clashes: Identical numbers cannot share an edge, even if they reside in different rooms.
• Vertical Hierarchy: If two cells are in the same room and stacked vertically, the top cell must have a strictly larger number than the bottom cell (top > bottom).

Deduction Strategies

Start by identifying all single-cell rooms (monominos) — they are instantly 1. Next, check vertical columns inside a room: if a room has a vertical tower of 3 cells, the numbers from top to bottom must strictly descend (e.g., 3 then 2 then 1). Use orthogonal elimination: placing a 1 blocks all 4 orthogonal neighbors from being 1.