Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution 2

Puzzles and Curious Problems by Henry Ernest Dudeney: $253$

The Angelica Puzzle

Draw a square with three lines in both direction and place on the intersecting points eight lettered counters as shown in our illustration.

The puzzle is to move the counters, one at a time, along the lines from point to vacant point until you get them in the order $\text {ANGELICA}$ thus:

$\begin{array} \\ A & N & G \\ E & L & I \\ C & A & .\end {array}$

Try to do this in the fewest possible moves.

Solution

Though we start with the $A$s in the correct positions, the puzzle can only be solved by making them change places.

Representing the $A$ in the bottom row with a capital, and the $A$ in the top corner with a small letter, the moves are as follows:

$\texttt {G E C a L N A C a L N A C a L I E G a L I E G I E N A E L a}$

which is $30$ moves in all.

There are $9$ more solutions with $30$ moves:

$\texttt {G E C a L N A C E G C E a I G a I L N A E C a I L N A E C a}$

$\texttt {G E L a C L A G E I L A G N a C A G N E I L G N E a C E L I}$

$\texttt {G E L N A L C I E G L C I a N A C I a E G L I a E N A E L I}$

$\texttt {G E L N A L E G L E C a N A E C a I G a I N A E C L a I L a}$

$\texttt {A E C a L N E C a I G a I L N E C A a I A C E A L N A E C a}$

$\texttt {A E G A E N L a C G A I G A N L a C A N L E I L E a C E L I}$

$\texttt {A E L a C L G I L G E A I L G E A N a C E A N a C E A N L I}$

$\texttt {A N L a C E G A N L a C E G A I G A L N I L N a C E A N L I}$

$\texttt {A N L a C E a L N a G A a N L C E G A I G A N L C E A N L a}$

Historical Note

The original solution found by Dudeney was of $36$ moves.

Martin Gardner reported on a $30$-move solution, but left it as an exercise for the reader to find.

Sources

• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $378$. The Angelica Puzzle