Henry Ernest Dudeney/Puzzles and Curious Problems/254 - The Flanders Wheel/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $254$

Place eight lettered counters on the wheel as shown.

Now move them one at a time along the line from circle to circle

until the word $\text {FLANDERS}$ can be correctly read round the rim of the wheel as at present,

only that the $\text F$ is in the upper circle now occupied by the $\text N$.

Of course two counters cannot be in a circle at the same time.

Find the fewest possible moves.

Move the counters in the following order:

$\texttt {A N D A F L N D A F D N L D R S D L N A F R S E R S L N A L}$

which is $30$ moves in all.

Move the counters in this order:

$\texttt {D N A D R E N R F S E N R F S L D A F S L D A L N E D N}$

or this order:

$\texttt {F S R F A L S A D N L S A D N E F R D N E F R E S L F S}$

which are both $28$ moves in all.

The $28$-move solution was reported on by Martin Gardner, who set it as a puzzle for his readers to solve.

He notes that it is isomorphic with a sliding-block puzzle of $8$ blocks on a $3 \times 3$ square array.

He then references his Mathematical Games columns in Scientific American for March and June $1965$.