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!
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).
|E| = |V| - 1
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 exactly using the determinant of the Laplacian matrix of the graph, discovered by Gustav Kirchhoff in 1847. Every puzzle generated in FluxLeft is a guaranteed unique, uniform spanning tree generated via randomized spanning tree algorithms.
Keyboard Shortcuts
- Left-Click / Tap : Rotate Clockwise ($+90^\circ$)
- Right-Click : Rotate Counter-Clockwise ($-90^\circ$)
- Z or Ctrl+Z : Undo
- Y or Ctrl+Y : Redo
- R : Reset current puzzle
- S : Reveal solution
- H : Hint
- M : Mute/Unmute audio