Number-degree bridges
Join all islands with one or two bridges so each island’s bridge count equals its printed number.
Logic & rule checking · Shape & spatial thinking
- Players
- 1–4 cooperative
- Time
- 12–20 minutes
- Materials and quantities
- Six labelled islands in two rows of three, seven candidate links, pencil.
1–4 cooperative
Prepare
Top row A,B,C has numbers 2,3,2; bottom row D,E,F has 2,3,2. Only these nearest straight links are available: AB,BC,DE,EF,AD,BE,CF. A link may carry zero, one or two bridges. Do not join diagonals or bypass an island.
Play
Write 0,1 or 2 on each candidate link. At an island, add the counts on incident links; the sum must equal that island’s number. Bridges are undirected and count at both ends. Ensure every island can be reached from every other through links with at least one bridge.
Example
One bridge on each of the seven links meets all degrees: A touches AB and AD for total 2; B touches AB,BC,BE for 3. Six islands split into disconnected smaller networks is not a solution even if each local total happens to match.
Finish
Check all six sums and trace one connected network. The teacher sheet gives a checked construction, not a promise of uniqueness. Different valid bridge counts are acceptable if they respect the same candidate links and every global rule.
Adapt
Use large line labels and a count table instead of drawing fine parallel lines. Work on local sums first, then connectivity. Do not call an unconnected set complete merely because all printed numbers were used.
Aim: Join all islands with one or two bridges so each island’s bridge count equals its printed number.
Practice within this activity: Join all islands with one or two bridges so each island’s bridge count equals its printed number.
Adult observation: Ask the participant to explain one legal choice. Accept passing and a partner writing; do not infer a lasting ability from a single round.
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: Draw six circles and the seven possible neighbour links on scrap paper.
Buying recommendations reserved; no purchase required.
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 six-island board
Top A B C: 2,3,2. Bottom D E F: 2,3,2. Only AB,BC,DE,EF,AD,BE,CF may have 0/1/2 bridges. All islands must connect. Grid coordinates are only positions; island letters are printed inside.
Player bridge counts
| Link | Bridges 0/1/2 |
|---|---|
| AB | ____ |
| BC | ____ |
| DE | ____ |
| EF | ____ |
| AD | ____ |
| BE | ____ |
| CF | ____ |
Teacher instructions and checked example · separate
1–4 cooperative
Six labelled islands in two rows of three, seven candidate links, pencil.
Draw six circles and the seven possible neighbour links on scrap paper.
Print only the relevant player pages; keep this teacher page separate. Read the full web rules before leading. A helper may write or move pieces, and anyone may pause or pass. No classroom or physical-printer trial is claimed.
| Link | Checked count |
|---|---|
| AB | 1 |
| BC | 1 |
| DE | 1 |
| EF | 1 |
| AD | 1 |
| BE | 1 |
| CF | 1 |
Degrees: A2,B3,C2,D2,E3,F2. All six nodes lie in one connected graph. This construction is one answer; never accept local totals without connectivity.