One Line Complete vs Euler's Circuit

Draw the whole shape in one continuous route, using every edge exactly once. One Line Complete is a clean one-stroke puzzle built from dots and lines. Choose a starting point, follow connected edges, and try to complete the entire figure without repeating the wrong path. The rule is simple, but each shape asks you to think about where to begin and where the route will end. Early levels are quick to solve. Later ones become real logic challenges, with more nodes, more branches, and less room for careless moves. Use observation, planning, and a little trial and error to find the path that finishes the drawing.

Trace every wire in a single stroke, and light up the circuit. Euler's Circuit is a quiet one-stroke (Eulerian circuit) puzzle. Tap or drag from node to node to trace the wires. Wherever there is only one way forward, the current runs on its own — the only thing you ever decide is which way to go at a fork. Designed not to tire you out - Straight runs auto-advance, so you only act where a real choice exists - Dead ends carry no penalty — you simply rewind to the last fork you chose - No lives, no game over, no timers - One set is five circuits: a complete session in about three minutes Clean solutions, not high scores - Three stars per circuit: finish it, finish without a dead end, finish without a hint - "Elegance" multiplies the wire count by Euler's number e (2.718…) for a flawless solve, or √e if you used a hint - New sets open as you complete them, growing larger and branchier - Daily Challenge: the same five circuits for everyone in the world, with a streak calendar - Game Center leaderboards for total stars and today's elegance The mathematics is the game Every circuit is generated so that each node has an even number of wires — by Euler's theorem, a solution always exists. A dead end only means your route stranded an island of wires behind you. The title spiral is an Euler spiral (clothoid). Background particles orbit the unit circle of e^(iθ), colors step around the hue wheel by 1/e, and the soundtrack is synthesized in real time using just intonation (1 : 9/8 : 5/4 : 3/2 : 5/3), with melodies walking the scale in the digits of e. Ads appear only between sets — never while you are tracing — and never in the Daily Challenge. The one-time Premium purchase removes them entirely.