Jade Grid Cascade

Jade Grid Cascade is a logic puzzle with two constraint systems running simultaneously — which makes every correct placement feel twice as good as Sudoku. A 6×6 grid sits on a dark canvas. Six geometric shapes float in the palette below: circle, triangle, square, pentagon, hexagon, star. Beside them: six colours — crimson, amber, jade, violet, ice, gold. The rules are split in two. Every row must contain each shape exactly once. Every column must contain each colour exactly once. And within each crystal zone — a thick-bordered 3×2 region — every shape and every colour must appear exactly once. Because shapes and colours are constrained independently, placing one pair eliminates options along two dimensions at the same time. A jade pentagon in row three removes all other pentagons from that row and all other jade from that column and all other pentagons and jade from its zone. Three separate eliminations from a single placement. This is why cells cascade. One correct placement often determines two or three others immediately — the puzzle clicks in a way that Sudoku rarely does. The cascade counter tracks how many empty cells are currently deducible from the constraints already in place. Watching it rise from two to five to nine after a well-chosen placement is the game's core satisfaction. Cells marked with a dashed jade ring have a unique valid pair that the current constraints determine completely. Finding these without the hint is the skill the game develops. Four puzzle modes. Harmony uses a 4×4 grid with four shapes and four colours — no crystal zones — and teaches the two-rule logic before adding the third constraint. Crystal is the full 6×6 game. Resonance introduces overlapping zones, where a single cell belongs to two crystal regions simultaneously and a wrong placement corrupts both. Prism scales to 8×8 with a diagonal rule that adds a fourth constraint dimension. The underlying mathematics is a Graeco-Latin square of order six: a grid where all thirty-six possible shape-colour pairs appear exactly once. Euler proved in 1782 that order-six Graeco-Latin squares were impossible. He was wrong, and the proof came in 1960. The puzzle the player is solving has a structure whose existence was controversial for nearly two centuries. When the grid is complete, the shapes in each row briefly sort themselves by number of sides — circle first, star last — before a wave of jade light rolls across the grid and every zone emits an expanding ring of geometric light simultaneously. It is the most satisfying solve animation in any logic puzzle on the platform.