Playfield Arcade

PAPER PRACTICE

Bridges: Build one network, not several finished pieces

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.

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CHALLENGE 1

Bridges study 7

ID: bridges-07 · Board: bridges-2027-08-01

Bridge networkB–A: 0 or 1 or 2 bridges; B–D: 0 or 1 or 2 bridges; C–B: 0 or 1 or 2 bridges; E–D: 0 or 1 or 2 bridges; F–G: 0 or 1 or 2 bridges; F–E: 0 or 1 or 2 bridgesA1B3C1D3E3F3G2

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-07/ · Personal, family and classroom printing permitted.

CHALLENGE 2

Bridges study 8

ID: bridges-08 · Board: bridges-2027-05-13

Bridge networkA–B: 0 or 1 or 2 bridges; C–B: 0 or 1 or 2 bridges; D–A: 0 or 1 or 2 bridges; E–C: 0 or 1 or 2 bridges; F–D: 0 or 1 or 2 bridges; F–G: 0 or 1 or 2 bridges; H–F: 0 or 1 or 2 bridgesA3B3C3D4E1F4G1H1

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-08/ · Personal, family and classroom printing permitted.

CHALLENGE 3

Bridges study 9

ID: bridges-09 · Board: bridges-2027-02-27

Bridge networkA–B: 0 or 1 or 2 bridges; C–A: 0 or 1 or 2 bridges; D–A: 0 or 1 or 2 bridges; D–G: 0 or 1 or 2 bridges; E–D: 0 or 1 or 2 bridges; E–F: 0 or 1 or 2 bridges; F–G: 0 or 1 or 2 bridges; H–I: 0 or 1 or 2 bridges; H–E: 0 or 1 or 2 bridges; I–C: 0 or 1 or 2 bridges; I–D: 0 or 1 or 2 bridgesA3B1C3D6E4F4G4H3I6

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-09/ · Personal, family and classroom printing permitted.

ANSWER 1

Bridges study 7

ID: bridges-07 · Board: bridges-2027-08-01

Bridge networkB–A: 1 bridge; B–D: 1 bridge; C–B: 1 bridge; E–D: 2 bridges; F–G: 2 bridges; F–E: 1 bridgeA1B3C1D3E3F3G2

Two checkpoints in the solution

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

playfieldarcade.com/practice/bridges/bridges-07/ · Personal, family and classroom printing permitted.

ANSWER 2

Bridges study 8

ID: bridges-08 · Board: bridges-2027-05-13

Bridge networkA–B: 1 bridge; C–B: 2 bridges; D–A: 2 bridges; E–C: 1 bridge; F–D: 2 bridges; F–G: 1 bridge; H–F: 1 bridgeA3B3C3D4E1F4G1H1

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

playfieldarcade.com/practice/bridges/bridges-08/ · Personal, family and classroom printing permitted.

ANSWER 3

Bridges study 9

ID: bridges-09 · Board: bridges-2027-02-27

Bridge networkA–B: 1 bridge; C–A: 1 bridge; D–A: 1 bridge; D–G: 2 bridges; E–D: 1 bridge; E–F: 2 bridges; F–G: 2 bridges; H–I: 2 bridges; H–E: 1 bridge; I–C: 2 bridges; I–D: 2 bridgesA3B1C3D6E4F4G4H3I6

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

playfieldarcade.com/practice/bridges/bridges-09/ · Personal, family and classroom printing permitted.