PuzzleTeam defines the rules as:
You have to draw lines between the dots to form a single loop without crossings or branches. The loop should pass through all black and white circles in such a way that:
How I actually solve one — the reasoning I run before any code does, written out in full. Read down the right column; the board on the left follows whichever step you are on.
A Shingoki board of side is really a lattice of dots, and the puzzle never asks me to fill a cell — it asks me to decide edges. Every unit segment between two adjacent dots is a boolean variable, drawn or crossed out, and there are of them. Enumerating outright would mean assignments — even the small daily carries 112 edge variables, so that route is dead on arrival.
One local law tames it. A closed loop enters and leaves every dot it visits, so each dot carries either no loop at all or exactly one way in and one way out:
That constraint comes with two immediate moves, and they carry most of the solve. A dot that already holds two drawn edges crosses out every other edge that touches it, and a dot with one drawn edge and a single open slot must continue through that slot. Everything that follows — circles, arithmetic, connectivity — exists mainly to feed those two moves new material.
The robotic solver on real boards: the daily puzzle comes straight from the API, and the samples — 5×5 · Easy up to 40×40 · Special — replay recorded solver runs move by move.