Cut or connect network
Compete over graph edges: one side claims an S–T path while the other removes possible links.
Logic & rule checking · Shape & spatial thinking
- Players
- 2 players
- Time
- 8–15 minutes
- Materials and quantities
- One supplied eleven-edge graph, two pen colours or claim/cut marks and a move log.
One graph per pair, with the move list available to both.
Prepare
Use nodes S, A, B, C, D, E, F and T and edges SA, SB, AC, AD, BD, BE, CF, DF, DT, ET and FT. These eleven listed edges are the whole graph; a crossing in a drawing is not an extra junction. One player is Connector, the other Cutter. Leave every edge initially unmarked. Symbols or distinct line patterns should distinguish claimed edges from removed edges without relying on colour alone.
Play
Connector moves first and claims one unmarked edge each turn. Cutter then removes one unmarked edge. An already claimed or removed edge cannot be selected again. Connector wins as soon as claimed edges alone connect S to T. Cutter wins as soon as no S–T route remains using claimed plus still-unmarked edges. The second check is about possibility: an unclaimed but available edge can keep the game alive.
Worked example
One legal, not necessarily optimal, sequence is claim SA, cut BE, claim AD, cut DT, claim DF, cut ET, claim FT. The claimed chain S–A–D–F–T then wins. Before FT was claimed, the chain was only a possible path, so it did not count as an earlier Connector win. The Cutter might have chosen better cuts; the sample demonstrates auditing, not a forced winning strategy.
Finish and check
After every move, check claimed connectivity and then possible connectivity. If no unmarked edge remains, exactly the appropriate path condition determines the outcome; do not award points for isolated claimed edges. Trace a claimed route with a finger or list its nodes to prove a win. For a cut win, show the group of nodes reachable from S through all unremoved edges and that T lies outside it.
Adaptation and practical limits
Swap roles for a second game because the goals are asymmetric. Work slowly on a copied diagram and agree that crossings are not nodes. A host can audit a claimed route but should not choose an edge. This is a paper model of a switching-game mechanism, not a live networking or security simulator. No connection to a real system is made.
Aim: Compete over graph edges: one side claims an S–T path while the other removes possible links.
Practice within this activity: Distinguish a currently owned path from a merely possible one.
Adult observation: Ask for a route or reachable-set explanation rather than assuming more marks means a win.
Mechanism and adaptation: A separately written PartyPageKit version of the mechanism described below, with original examples and materials. The earliest inventor is not established here.
Goals describe observable activity choices, not measured long-term gains or institutional endorsement.
Free alternatives: Use paper or clean reused cardboard and a pencil. Copy the supplied diagrams and tables by hand; no specialist kit or purchase is needed.
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.
Player switching graph
Thick/claimed and dashed/cut; crossings are not nodes. Only the eleven drawn/listed edges exist.
Edges: SA SB AC AD BD BE CF DF DT ET FT.
Player route and reachable-set log
| Turn | Claim / cut | Owned S–T? | Still possible? |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host / teacher checked example · separate
One graph per pair, with the move list available to both.
One supplied eleven-edge graph, two pen colours or claim/cut marks and a move log.
Keep this answer page separate. Read the full web rules and preview materials before leading; allow pauses, passing and supported writing.
Legal illustration: +SA −BE +AD −DT +DF −ET +FT. Final owned route S–A–D–F–T. This illustrates legal auditing, not best play.