The fewest possible moves for getting the prisoners into their dungeons
in the required numerical order are twenty-six. 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.
[Illustration]
The diagram may be simplified by my "buttons and string" method, fully
explained in _A. in M._, p. 230. 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
[Illustration:
{1 2 3}
{4 5 6}
{7 8 } ]
in the fewest possible moves.
See also solution to No. 94.