How to play

Euler

Euler levels (1 to 9)

Run the rope along every thread without repeating any and without lifting it. You need not return to the first nail, but if the level has two odd nails you must start at one of them.

A connected graph can be drawn in one stroke when it has zero or two vertices of odd degree. Euler proved it in 1736 with the bridges of Königsberg.

Hamilton

Hamilton levels (10 to 15)

Visit every nail exactly once and come back to the starting nail. You do not need every thread, just close the circuit.

Finding a Hamiltonian cycle is NP-complete: no quick rule tells you whether one exists, you have to search for it.

Controls

Drag from the active nail: the rope jumps to whichever nail you aim at.
Or tap nail by nail if you prefer precision.
Drag back over the previous nail to undo the last stretch.
Keyboard: Z undoes, R restarts, H gives a hint.
Crossing threads is allowed: what counts is where the rope goes.