Weighted bridge network: rules and printable materials

Choose a low-cost set of edges that connects every location, allowing branches.

Players

1–6 (cooperative)

Plan for

15–20 minutes

Bring

Five-node map, edge-cost list and connection log

Use only listed bridges

The five locations are A, B, C, D and E. Available undirected bridges and costs are AB=2, AC=4, BC=1, BD=5, CD=3, CE=6 and DE=2. A bridge can be used in either direction and paid for once. No other pair has a bridge. Costs are fictional tokens, not distances or real construction estimates. Start with all five locations separate.

Connect the whole network

Choose bridges until every pair of locations can reach one another through selected bridges. You may branch at a location, and no single walking route has to visit everything once. An isolated E makes the plan invalid even if A–D are cheaply connected. Draw the selected edges and add each listed cost exactly once. Adding a second copy of AB does not improve connectivity.

Check a proposed plan

AB, BC, CD and DE connect all five locations for 2+1+3+2=8. Starting at E, one can reach D, C, B and A. AC, BC, CD and DE also connect everyone but cost 10. A cheaper-looking set AB, BC and DE costs 5 yet leaves two disconnected groups, so it is not a solution. Verify reachability before comparing prices.

Reason about the minimum

Five separate locations require at least four connecting bridges. One useful method considers the cheapest available edge and adds it only if it joins two previously disconnected groups; continue until one group remains. For this map, BC, AB, DE and CD form the cost-8 result. This is a minimum spanning tree exercise under the stated undirected positive costs. It is not a shortest-path problem between only A and E.

Discuss without time pressure

Give each participant a role: propose an edge, check a cost or trace connectivity. Keep unsuccessful proposals on a separate log instead of claiming every drawn line is bought. A helper may trace the path or read the edge list. Stop when the group has a connected plan and can justify the best total, then compare with the separate key. The printed map has no automatic checker or animated network.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.