The Objective

The central Power Core emits high-voltage plasma energy. Rotate the conduit tiles until every single node in the network is energized with zero disconnected leaks!

Linked Gears (5×5 and up)

Tiles with the same gold letter form a pair. Tap either tile to turn it clockwise while its partner turns counter-clockwise. Right-click reverses both. Plan the two ends together: fixing one connection can break another. Unmarked tiles rotate independently. One pair starts at 5×5, increasing to eight pairs at 16×16.

Hints highlight both partners and tell you which tile to tap and how many times. Undo and redo restore the entire move. Reset restores the original scramble; Reveal uses legal linked moves and can be undone. Revealed puzzles do not earn best-time records.

What is a Spanning Tree?

In graph theory, a Spanning Tree of a connected graph G = (V, E) is a subgraph that includes all vertices of G, is completely connected, and contains no cycles (no closed loops).

For any grid of N tiles, a valid energized circuit contains exactly N - 1 mutual connections. This mathematical principle guarantees that there is no wasted energy circulating in redundant loops.

Kirchhoff's Matrix Tree Theorem

The number of distinct spanning trees on a grid can be computed using the determinant of a reduced Laplacian matrix. FluxLeft generates a spanning tree with randomized Kruskal's algorithm, then scrambles it using legal rotations. This guarantees a reachable solution, including all linked gears; it does not promise a unique solution or a uniform sample of all trees.