A 50-YEAR-OLD MATHEMATICAL MYSTERY

Can every road
belong to two
perfect loops?

One simple-sounding question. Still no proof.

SCROLL TO EXPLORE

01 — THE ONE RULE

No road may be a bridge.

A bridge is the only way between two places. Remove it, and the map falls into two separate worlds.

One fragile road holds the map together.

02 — FIND YOUR WAY HOME

A cycle is a route that closes.

Start anywhere. Follow roads without turning around. If you return to the start, you made a cycle.

03 — YOUR TURN

Cover every road exactly twice.

0of 9 roads
covered twice

Select loops. Number on each road shows its coverage.

THE CYCLE DOUBLE COVER CONJECTURE

We can solve this map.
Can we solve every map?

Mathematicians conjecture that every bridgeless graph has a collection of cycles covering each edge exactly twice. Nobody has proved it. Nobody has found a counterexample.

Walk it again ↑