Henry Ernest Dudeney/Modern Puzzles/191 - Crossing the Ferry/Solution

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Modern Puzzles by Henry Ernest Dudeney: $191$

Crossing the Ferry
Six persons, all related, have to cross a river in a small boat that will only hold two.
Mr. Webster, who had to plan the little affair, had quarrelled with his father-in-law and his son,
and, I am sorry to say, Mrs. Webster was not on speaking terms with her mother or her daugther-in-law.
In fact, the relations were so strained that it was not safe to permit any of the belligerents to pass over together
or to remain together on the same side of the river.
And to prevent further discord, no man was to be left with two women or two men with three women.
How are they to perform the feat in the fewest possible crossings?
No tricks, such as making use of a rope or current, or swimming across, are allowed.


Solution

First let us establish who we have here, and assign them labels, according to seniority and gender:

$(1): \quad$ Mrs. Webster's mother and her husband: let them be labelled $A$ and $X$ (Adrienne and Xavier)
$(2): \quad$ Mr. Webster and his wife Mrs. Webster: let them be labelled $B$ and $Y$ (Bertram and Yvonne)
$(3): \quad$ Mr. and Mrs. Webster's son and his wife: let them be labelled $C$ and $Z$ (Colin and Zoe)

Hence the rules state:

$B$ cannot share a boat, or remain together on the same side as either $A$ or $C$.
$Y$ cannot share a boat, or remain together on the same side as either $X$ or $Z$.
Men must not be outnumbered by women at any stage.


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

$\begin {array} {r c| c l}

A B C \ X Y Z & \bullet & & \\ A C \ X Z & & \bullet & B \ Y \\ A C \ X Y Z & \bullet & & B\\ A C \ Y & & \bullet & B \ X Z \\ A B C \ Y & \bullet & & X Z \\ B \ Y & & \bullet & A C \ X Z \\ B \ Y Z & \bullet & & A C \ X \\ Y & & \bullet & A B C \ X Z \\ B Y & \bullet & & A C \ X Z \\ & & \bullet & A B C \ X Y Z \end{array}$


Sources

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