Henry Ernest Dudeney/Modern Puzzles/192 - Missionaries and Cannibals/Solution

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Modern Puzzles by Henry Ernest Dudeney: $192$

Missionaries and Cannibals
There is a strange story of three missionaries and three cannibals,
who had to cross a river in a small boat that would only carry two men at a time.
Being acquainted with the peculiar appetites of the cannibals,
the missionaries could never allow their companions to be in a majority on either side of the river.
Only one of the missionaries and one of the cannibals could row the boat.
How did they manage to get across?


Solution

Let the missionaries be labelled $M$, $m$ and $m$.

Let the cannibals be labelled $C$, $c$ and $c$.

In both cases the capital letters indicate who is able to row.


Here they are at each stage of the crossing, where the bullet indicates where the boat is:

$\begin {array} {l | r c| c l}
 & M m m \ C c c & \bullet &  & \\

1 & M m m \ c & & \bullet & C c \\ 2 & M m m \ C c & \bullet & & c\\ 3 & M m m & & \bullet & C c c \\ 4 & M m m \ C & \bullet & & c c \\ 5 & m \ C & & \bullet & M m \ c c \\ 6 & M m \ C c & \bullet & & m \ c \\ 7 & m \ c & & \bullet & M m \ C c \\ 8 & M m \ c c & \bullet & & m \ C \\ 9 & c c & & \bullet & M m m \ C \\ 10 & C c c & \bullet & & M m m \\ 11 & c & & \bullet & M m m \ C c \\ 12 & C c & \bullet & & M m m \ c \\ 13 & & & \bullet & M m m \ C c c \\ \end{array}$


Historical Note

Martin Gardner reports on a graphical technique for solving such questions.

He cites a $1966$ article in Mathematics Magazine, and also 1965: T.H. O'Beirne: Puzzles and Paradoxes.


Sources

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