Playfield Arcade

PAPER PRACTICE

Bridges: Count the available bridges

Three fixed studies, followed by separate answer pages. The links and IDs match the online collection.

Join nearest visible islands horizontally or vertically with zero, one or two bridges per route. A bridge cannot pass through an island or cross another bridge between islands. Each island’s number counts individual bridges, and all islands must belong to one connected network.

Use your browser’s Print command or Save as PDF. Both A4 and US Letter fit the diagrams. To keep answers separate, print only the challenge pages. The answer pages contain two useful checkpoints; the online practice page contains the complete checked route.

Return to the online collection

CHALLENGE 1

Bridges study 1

ID: bridges-01 · Board: bridges-2027-01-13

Bridge networkA–F: 0 or 1 or 2 bridges; B–A: 0 or 1 or 2 bridges; B–C: 0 or 1 or 2 bridges; C–D: 0 or 1 or 2 bridges; D–E: 0 or 1 or 2 bridges; F–G: 0 or 1 or 2 bridges; G–E: 0 or 1 or 2 bridgesA4B3C3D3E2F2G1

Explain one move you can prove. Which displayed clue or rule supports it?

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-01/ · Personal, family and classroom printing permitted.

CHALLENGE 2

Bridges study 2

ID: bridges-02 · Board: bridges-2027-05-12

Bridge networkA–B: 0 or 1 or 2 bridges; A–C: 0 or 1 or 2 bridges; B–D: 0 or 1 or 2 bridges; C–E: 0 or 1 or 2 bridges; D–E: 0 or 1 or 2 bridges; F–D: 0 or 1 or 2 bridges; G–F: 0 or 1 or 2 bridgesA3B4C2D5E2F3G1

Explain one move you can prove. Which displayed clue or rule supports it?

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-02/ · Personal, family and classroom printing permitted.

CHALLENGE 3

Bridges study 3

ID: bridges-03 · Board: bridges-2027-05-17

Bridge networkA–B: 0 or 1 or 2 bridges; A–C: 0 or 1 or 2 bridges; B–E: 0 or 1 or 2 bridges; C–D: 0 or 1 or 2 bridges; F–E: 0 or 1 or 2 bridges; G–D: 0 or 1 or 2 bridgesA4B4C3D3E4F2G2

Explain one move you can prove. Which displayed clue or rule supports it?

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-03/ · Personal, family and classroom printing permitted.

ANSWER 1

Bridges study 1

ID: bridges-01 · Board: bridges-2027-01-13

Bridge networkA–F: 2 bridges; B–A: 2 bridges; B–C: 1 bridge; C–D: 2 bridges; D–E: 1 bridge; F–G: 0 bridges; G–E: 1 bridge×A4B3C3D3E2F2G1

Two checkpoints in the solution

  1. Island A needs 4 individual bridges. Its routes currently allow 0 to 4 in total. Holding the other routes within their limits restricts A–F to 2; B–A to 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
  2. Island B needs 3 individual bridges. Its routes currently allow 2 to 4 in total. Holding the other routes within their limits restricts B–C to 1. A domain “1 or 2” proves a connection but does not yet choose single or double.

playfieldarcade.com/practice/bridges/bridges-01/ · Personal, family and classroom printing permitted.

ANSWER 2

Bridges study 2

ID: bridges-02 · Board: bridges-2027-05-12

Bridge networkA–B: 2 bridges; A–C: 1 bridge; B–D: 2 bridges; C–E: 1 bridge; D–E: 1 bridge; F–D: 2 bridges; G–F: 1 bridgeA3B4C2D5E2F3G1

Two checkpoints in the solution

  1. Removing F–D would split the graph of all still-possible routes. Every island must belong to one network, so F–D must carry at least one bridge. This does not by itself decide between one and two.
  2. Removing G–F would split the graph of all still-possible routes. Every island must belong to one network, so G–F must carry at least one bridge. This does not by itself decide between one and two.

playfieldarcade.com/practice/bridges/bridges-02/ · Personal, family and classroom printing permitted.

ANSWER 3

Bridges study 3

ID: bridges-03 · Board: bridges-2027-05-17

Bridge networkA–B: 2 bridges; A–C: 2 bridges; B–E: 2 bridges; C–D: 1 bridge; F–E: 2 bridges; G–D: 2 bridgesA4B4C3D3E4F2G2

Two checkpoints in the solution

  1. Removing A–B would split the graph of all still-possible routes. Every island must belong to one network, so A–B must carry at least one bridge. This does not by itself decide between one and two.
  2. Removing A–C would split the graph of all still-possible routes. Every island must belong to one network, so A–C must carry at least one bridge. This does not by itself decide between one and two.

playfieldarcade.com/practice/bridges/bridges-03/ · Personal, family and classroom printing permitted.