Euler's Circuit - One Line

Straight runs trace themselves — you only ever choose at a fork. Five circuits per set, about three minutes a session, and a dead end costs you nothing.

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.