Kirchhoff

FLOW IN, FLOW OUT

Tap an edge to cycle through the two directions and back to nothing.

FLOW IN, FLOW OUT

Kirchhoff

Named after Kirchhoff's law of current: what flows into a node must flow back out. This puzzle applies that law to a grid — every cell balances its own books, and that alone is enough to fix one arrangement of arrows.

RULES

  • A circled number is a source (+) or a sink (−) with that much to send or absorb.
  • A plain number is throughput: how many arrows enter that cell, which is also how many leave.
  • Every other cell takes in exactly as much as it gives out.

CONTROLS

  • Tap an edge to cycle through the two directions and back to nothing.
constructing a layout…

Related: Slitherlink, another loop-and-parity puzzle solved by the same connectivity toolkit, and Arbour, another puzzle built on a spanning structure rather than a search.