Graph Theory · Explore together

Can you trace it?

Build a network, predict a one-stroke route, and trade puzzles with a partner.

One person controls the experiment. The other predicts and questions. Swap roles after a trial.

∑v∈Vdeg⁡(v)=2∣E∣\sum_{v\in V}\deg(v)=2|E|

Predict before tracing. Can you use every edge once? Agree on a starting vertex with your partner, then test your route.

9 edges · ready to test

Choose a prediction, then start your route.

Build or change the network

Toggle a connection. Crossings are not new vertices.

You may revisit a vertex. Each edge may be used once. To edit again, clear the route.

Trade a puzzle. Change one edge, ask your partner to predict the effect, and explain what happens at its two ends.

Compare your evidence

What can you explain now?

Ask your partner to restate your reasoning. An experiment suggests a pattern; your explanation should say why it holds and when it applies.

  1. How does entering and leaving a vertex account for its degree?
  2. Why do connectivity and odd degrees both matter?
  3. Change one edge. What changes in your argument?