expert Set 21 Logic Puzzle

Expert River Crossing Puzzle #21

Show solution

[{"trip":1,"direction":"\u2192","carrying":["C","C"],"leftBank":"3M 1C","rightBank":"0M 2C","note":"2 cannibals cross."},{"trip":2,"direction":"\u2190","carrying":["C"],"leftBank":"3M 2C","rightBank":"0M 1C","note":"1 cannibal returns."},{"trip":3,"direction":"\u2192","carrying":["C","C"],"leftBank":"3M 0C","rightBank":"0M 3C","note":"2 cannibals cross."},{"trip":4,"direction":"\u2190","carrying":["C"],"leftBank":"3M 1C","rightBank":"0M 2C","note":"1 cannibal returns."},{"trip":5,"direction":"\u2192","carrying":["M","M"],"leftBank":"1M 1C","rightBank":"2M 2C","note":"2 missionaries cross."},{"trip":6,"direction":"\u2190","carrying":["M","C"],"leftBank":"2M 2C","rightBank":"1M 1C","note":"1M + 1C return."},{"trip":7,"direction":"\u2192","carrying":["M","M"],"leftBank":"0M 2C","rightBank":"3M 1C","note":"2 missionaries cross."},{"trip":8,"direction":"\u2190","carrying":["C"],"leftBank":"0M 3C","rightBank":"3M 0C","note":"1 cannibal returns."},{"trip":9,"direction":"\u2192","carrying":["C","C"],"leftBank":"0M 1C","rightBank":"3M 2C","note":"2 cannibals cross."},{"trip":10,"direction":"\u2190","carrying":["C"],"leftBank":"0M 2C","rightBank":"3M 1C","note":"1 cannibal returns."},{"trip":11,"direction":"\u2192","carrying":["C","C"],"leftBank":"0M 0C","rightBank":"3M 3C","note":"2 cannibals cross. Done!"}]

Title
Expert River Crossing Puzzle #21
Scenario
Missionaries & Cannibals
Narrative
Three missionaries and three cannibals must cross a river. The boat holds at most 2 people. At no time may cannibals outnumber missionaries on either bank (or the missionaries will be in danger).
Entities
  • {"id":"m1","name":"Missionary 1","icon":"\ud83d\ude4f"}
  • {"id":"m2","name":"Missionary 2","icon":"\ud83d\ude4f"}
  • {"id":"m3","name":"Missionary 3","icon":"\ud83d\ude4f"}
  • {"id":"c1","name":"Cannibal 1","icon":"\u2694\ufe0f"}
  • {"id":"c2","name":"Cannibal 2","icon":"\u2694\ufe0f"}
  • {"id":"c3","name":"Cannibal 3","icon":"\u2694\ufe0f"}
BoatCapacity
2
Constraints
  • The boat holds at most 2 people.
  • On either bank, cannibals must not outnumber missionaries (unless no missionaries are present).
  • At least one person must row the boat each trip.
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":["C","C"],"leftBank":"3M 1C","rightBank":"0M 2C","note":"2 cannibals cross."}
  • {"trip":2,"direction":"\u2190","carrying":["C"],"leftBank":"3M 2C","rightBank":"0M 1C","note":"1 cannibal returns."}
  • {"trip":3,"direction":"\u2192","carrying":["C","C"],"leftBank":"3M 0C","rightBank":"0M 3C","note":"2 cannibals cross."}
  • {"trip":4,"direction":"\u2190","carrying":["C"],"leftBank":"3M 1C","rightBank":"0M 2C","note":"1 cannibal returns."}
  • {"trip":5,"direction":"\u2192","carrying":["M","M"],"leftBank":"1M 1C","rightBank":"2M 2C","note":"2 missionaries cross."}
  • {"trip":6,"direction":"\u2190","carrying":["M","C"],"leftBank":"2M 2C","rightBank":"1M 1C","note":"1M + 1C return."}
  • {"trip":7,"direction":"\u2192","carrying":["M","M"],"leftBank":"0M 2C","rightBank":"3M 1C","note":"2 missionaries cross."}
  • {"trip":8,"direction":"\u2190","carrying":["C"],"leftBank":"0M 3C","rightBank":"3M 0C","note":"1 cannibal returns."}
  • {"trip":9,"direction":"\u2192","carrying":["C","C"],"leftBank":"0M 1C","rightBank":"3M 2C","note":"2 cannibals cross."}
  • {"trip":10,"direction":"\u2190","carrying":["C"],"leftBank":"0M 2C","rightBank":"3M 1C","note":"1 cannibal returns."}
  • {"trip":11,"direction":"\u2192","carrying":["C","C"],"leftBank":"0M 0C","rightBank":"3M 3C","note":"2 cannibals cross. Done!"}
MinimumTrips
11
Hint
No hints are provided for this difficulty. Find the full solution on your own.
PartialSolutionHint