Playfield Arcade

PAPER PRACTICE

Bridges: Track the consequences of a connection

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 4

ID: bridges-04 · Board: bridges-2027-07-15

Bridge networkA–C: 0 or 1 or 2 bridges; B–F: 0 or 1 or 2 bridges; B–A: 0 or 1 or 2 bridges; C–D: 0 or 1 or 2 bridges; E–C: 0 or 1 or 2 bridges; F–E: 0 or 1 or 2 bridges; F–G: 0 or 1 or 2 bridges; H–G: 0 or 1 or 2 bridges; H–I: 0 or 1 or 2 bridges; I–D: 0 or 1 or 2 bridgesA4B3C6D3E2F2G3H2I1

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-04/ · Personal, family and classroom printing permitted.

CHALLENGE 2

Bridges study 5

ID: bridges-05 · Board: bridges-2027-07-28

Bridge networkA–C: 0 or 1 or 2 bridges; A–F: 0 or 1 or 2 bridges; B–E: 0 or 1 or 2 bridges; B–A: 0 or 1 or 2 bridges; C–G: 0 or 1 or 2 bridges; D–C: 0 or 1 or 2 bridges; E–D: 0 or 1 or 2 bridges; E–H: 0 or 1 or 2 bridges; F–H: 0 or 1 or 2 bridges; H–G: 0 or 1 or 2 bridgesA5B2C5D3E1F2G3H3

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-05/ · Personal, family and classroom printing permitted.

CHALLENGE 3

Bridges study 6

ID: bridges-06 · Board: bridges-2027-07-25

Bridge networkA–B: 0 or 1 or 2 bridges; A–C: 0 or 1 or 2 bridges; B–G: 0 or 1 or 2 bridges; C–D: 0 or 1 or 2 bridges; D–G: 0 or 1 or 2 bridges; D–F: 0 or 1 or 2 bridges; E–J: 0 or 1 or 2 bridges; E–A: 0 or 1 or 2 bridges; H–B: 0 or 1 or 2 bridges; I–F: 0 or 1 or 2 bridges; J–H: 0 or 1 or 2 bridges; J–D: 0 or 1 or 2 bridgesA6B5C3D3E3F3G2H3I2J2

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

Reason: ____________________________________________________

___________________________________________________________

playfieldarcade.com/practice/bridges/bridges-06/ · Personal, family and classroom printing permitted.

ANSWER 1

Bridges study 4

ID: bridges-04 · Board: bridges-2027-07-15

Bridge networkA–C: 2 bridges; B–F: 1 bridge; B–A: 2 bridges; C–D: 2 bridges; E–C: 2 bridges; F–E: 0 bridges; F–G: 1 bridge; H–G: 2 bridges; H–I: 0 bridges; I–D: 1 bridge××A4B3C6D3E2F2G3H2I1

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–C to 2; B–A to 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
  2. A–C is established with at least one bridge. H–I cross that route between islands, so they must carry zero bridges.

playfieldarcade.com/practice/bridges/bridges-04/ · Personal, family and classroom printing permitted.

ANSWER 2

Bridges study 5

ID: bridges-05 · Board: bridges-2027-07-28

Bridge networkA–C: 2 bridges; A–F: 1 bridge; B–E: 0 bridges; B–A: 2 bridges; C–G: 1 bridge; D–C: 2 bridges; E–D: 1 bridge; E–H: 0 bridges; F–H: 1 bridge; H–G: 2 bridges××A5B2C5D3E1F2G3H3

Two checkpoints in the solution

  1. Island A needs 5 individual bridges. Its routes currently allow 0 to 6 in total. Holding the other routes within their limits restricts A–C to 1 or 2; A–F to 1 or 2; B–A to 1 or 2. A domain “1 or 2” proves a connection but does not yet choose single or double.
  2. A–C is established with at least one bridge. E–H cross that route between islands, so they must carry zero bridges.

playfieldarcade.com/practice/bridges/bridges-05/ · Personal, family and classroom printing permitted.

ANSWER 3

Bridges study 6

ID: bridges-06 · Board: bridges-2027-07-25

Bridge networkA–B: 2 bridges; A–C: 2 bridges; B–G: 1 bridge; C–D: 1 bridge; D–G: 1 bridge; D–F: 1 bridge; E–J: 1 bridge; E–A: 2 bridges; H–B: 2 bridges; I–F: 2 bridges; J–H: 1 bridge; J–D: 0 bridges×A6B5C3D3E3F3G2H3I2J2

Two checkpoints in the solution

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

playfieldarcade.com/practice/bridges/bridges-06/ · Personal, family and classroom printing permitted.