Once upon a time there was a city that had no roads. Getting around the city was particularly difficult after a rainstorm because the ground became very muddy—cars got stuck in the mud and people got their boots dirty. The mayor of the city decided that some of the streets should be paved, but he didn’t want to spend more money than necessary because the city also wanted to build a swimming pool. The mayor therefore specified two conditions:
1. Enough streets must be paved so that everyone can travel from their house to anyone else’s house only along paved roads.
2. The paving should cost as little as possible.
Here is the layout of the city. The number of paving stones between each house represents the cost of paving that route. Find the best route that connects all the houses, but uses as few counters (paving stones) as possible.
