I was in my second of three grade schools when my math teacher gave this problem [3 Cannibals and 3 Missionaries have to cross a river with a boat that holds two at a time; Cannibals cannot ever outnumber Missionaries, etc.] to my class. We pounded away at it for days. During that time I saw every wrong answer and blind alley imaginable; even came up with a solution of my own, which I was totally confident with, that was totally wrong (forgot to account for the boat passengers…very common stumbling block).
Later that semester, I saw the solution in one of those index card-style puzzle collections, but for some reason I never bothered to work it out. (This collection, BTW, stipulated that only one of the cannibals knew how to row the boat, a provision I’d never seen before.)
Years later, and far removed from tackling childhood puzzles, I think about this problem. And I hit upon the solution. In about fifteen seconds.
On to my questions:
How did I nail the solution so quickly? I was never all that good at these kind of problems…I blew the doubling lily pad question and got my thinking completely bass-ackwards on the “half your bread plus half a loaf” problem. I’m not a whole lot better at logic than I was a decade ago, either.
Is the correct version of the problem the one where only one cannibal can row? It doesn’t affect the solution much, but it does make the process more complicated (you gotta keep track of which side that important cannibal is on). I just want to know if that was the intention.
Why missionaries? They’d seem to be an unusual choice for a children’s puzzle, especially consorting with people as unsavory as cannibals.
[Aside: Games magazine once printed someone’s joke based on this choice - “Three cannibals and three missionaries have to cross a river using a boat that can only seat two at a time. However, there must never be a situation with two missionaries and one cannibal, because the missionaries are constantly demonstrating the “Missionary Position”, and the cannibals are sick of it.”]