Answer
The fewest possible
moves for getting the
prisoners into their
dungeons
in the required numerical order are twentysix.
The men move in the
following order:—1, 2, 3, 1, 2, 6, 5, 3, 1, 2, 6, 5, 3, 1, 2,
4, 8, 7,
1, 2, 4, 8, 7, 4, 5, 6.
As there are never
more than
one vacant dungeon
to be moved into, there can be no ambiguity in the notation.
The diagram may be simplified by my "buttons and
string"
method.
It then takes one of
the simple forms of
A or B, and the solution is much easier.
In A we use counters; in B we
can employ rooks on a corner of a chessboard.
In both cases we have to
get the order
in the fewest possible moves.
