River Crossing River Missionary Cannibal Hard — Set 27

Hard River Crossing Puzzle #27

Title

Hard River Crossing Puzzle #27

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

The first 1 move(s) of the solution are shown below to help you start.

PartialSolutionHint

• {"trip":1,"direction":"\u2192","carrying":["C","C"],"leftBank":"3M 1C","rightBank":"0M 2C","note":"2 cannibals cross."}