expert Set 5 Logic Puzzle

Expert River Crossing Puzzle #5

Show solution

[{"trip":1,"direction":"\u2192","carrying":["K1","S1"],"leftBank":"2K 2S","rightBank":"1K 1S","note":"1 knight + 1 squire cross."},{"trip":2,"direction":"\u2190","carrying":["K1"],"leftBank":"3K 2S","rightBank":"0K 1S","note":"Knight returns."},{"trip":3,"direction":"\u2192","carrying":["K1","K2"],"leftBank":"1K 2S","rightBank":"2K 1S","note":"2 knights cross."},{"trip":4,"direction":"\u2190","carrying":["K1","S1"],"leftBank":"2K 3S","rightBank":"1K 0S","note":"K + S return."},{"trip":5,"direction":"\u2192","carrying":["S1","S2"],"leftBank":"2K 1S","rightBank":"1K 2S","note":"2 squires cross."},{"trip":6,"direction":"\u2190","carrying":["K2","S2"],"leftBank":"3K 2S","rightBank":"0K 1S","note":"K + S return."},{"trip":7,"direction":"\u2192","carrying":["K2","K3"],"leftBank":"1K 2S","rightBank":"2K 1S","note":"2 knights cross."},{"trip":8,"direction":"\u2190","carrying":["K3"],"leftBank":"2K 2S","rightBank":"1K 1S","note":"Knight returns."},{"trip":9,"direction":"\u2192","carrying":["K3","S3"],"leftBank":"1K 1S","rightBank":"2K 2S","note":"K + S cross."},{"trip":10,"direction":"\u2190","carrying":["K3"],"leftBank":"2K 1S","rightBank":"1K 2S","note":"Knight returns."},{"trip":11,"direction":"\u2192","carrying":["K3","S2"],"leftBank":"1K 0S","rightBank":"2K 3S","note":"K + S cross."},{"trip":12,"direction":"\u2190","carrying":["K1"],"leftBank":"2K 0S","rightBank":"1K 3S","note":"Knight returns."},{"trip":13,"direction":"\u2192","carrying":["K1","S1"],"leftBank":"1K 0S","rightBank":"2K 4S","note":"K + S cross."}]

Title
Expert River Crossing Puzzle #5
Scenario
Knights & Squires
Narrative
Three knights and three squires must cross a river. The boat holds 2. If squires outnumber knights on either bank, the squires rebel.
Entities
  • {"id":"k1","name":"Knight 1","icon":"\u2694\ufe0f"}
  • {"id":"k2","name":"Knight 2","icon":"\u2694\ufe0f"}
  • {"id":"k3","name":"Knight 3","icon":"\u2694\ufe0f"}
  • {"id":"s1","name":"Squire 1","icon":"\ud83d\udee1\ufe0f"}
  • {"id":"s2","name":"Squire 2","icon":"\ud83d\udee1\ufe0f"}
  • {"id":"s3","name":"Squire 3","icon":"\ud83d\udee1\ufe0f"}
BoatCapacity
2
Constraints
  • Boat capacity: 2 people.
  • On either bank, squires must not outnumber knights (unless no knights are present).
Question
Describe a valid sequence of crossings that gets everyone to the other side without violating any constraint. What is the minimum number of trips required?
Solution
  • {"trip":1,"direction":"\u2192","carrying":["K1","S1"],"leftBank":"2K 2S","rightBank":"1K 1S","note":"1 knight + 1 squire cross."}
  • {"trip":2,"direction":"\u2190","carrying":["K1"],"leftBank":"3K 2S","rightBank":"0K 1S","note":"Knight returns."}
  • {"trip":3,"direction":"\u2192","carrying":["K1","K2"],"leftBank":"1K 2S","rightBank":"2K 1S","note":"2 knights cross."}
  • {"trip":4,"direction":"\u2190","carrying":["K1","S1"],"leftBank":"2K 3S","rightBank":"1K 0S","note":"K + S return."}
  • {"trip":5,"direction":"\u2192","carrying":["S1","S2"],"leftBank":"2K 1S","rightBank":"1K 2S","note":"2 squires cross."}
  • {"trip":6,"direction":"\u2190","carrying":["K2","S2"],"leftBank":"3K 2S","rightBank":"0K 1S","note":"K + S return."}
  • {"trip":7,"direction":"\u2192","carrying":["K2","K3"],"leftBank":"1K 2S","rightBank":"2K 1S","note":"2 knights cross."}
  • {"trip":8,"direction":"\u2190","carrying":["K3"],"leftBank":"2K 2S","rightBank":"1K 1S","note":"Knight returns."}
  • {"trip":9,"direction":"\u2192","carrying":["K3","S3"],"leftBank":"1K 1S","rightBank":"2K 2S","note":"K + S cross."}
  • {"trip":10,"direction":"\u2190","carrying":["K3"],"leftBank":"2K 1S","rightBank":"1K 2S","note":"Knight returns."}
  • {"trip":11,"direction":"\u2192","carrying":["K3","S2"],"leftBank":"1K 0S","rightBank":"2K 3S","note":"K + S cross."}
  • {"trip":12,"direction":"\u2190","carrying":["K1"],"leftBank":"2K 0S","rightBank":"1K 3S","note":"Knight returns."}
  • {"trip":13,"direction":"\u2192","carrying":["K1","S1"],"leftBank":"1K 0S","rightBank":"2K 4S","note":"K + S cross."}
MinimumTrips
13
Hint
No hints are provided for this difficulty. Find the full solution on your own.
PartialSolutionHint