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It's a Metric, Too

Unofficial practice boards for Jane Street's October 2026 puzzle. Every generated board has exactly one solution. To see where capitols might sit, try the capitol magnets.

Board

Drag to paint squares. Neighbouring states need different colors, since touching squares of one color count as one state.

Rules

Split the grid into states: connected groups of squares, each symmetric under some rotation or reflection.
A state has a capitol when every non-trivial symmetry of it fixes exactly one square; that square is the capitol. A 1×3 bar and the X pentomino have none. A single square is its own capitol.
Moving to an orthogonal neighbour costs the size of the state you are in. Crossing a border between two states costs the smaller of the two sizes.
A number is the cheapest total cost from that square to any capitol, so a 0 marks a capitol.
Answer: label every square with its state's size, sum each row, and add up the squares of the row sums.

Keys: 1–9 and 0 pick colors, C capitol, E eraser, Ctrl+Z undo. The 11×11 board is the original puzzle; Check tells you whether your grid satisfies every rule and clue.