Henry Ernest Dudeney/Puzzles and Curious Problems/253 - The Angelica Puzzle/Solution 1

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:

$A \ N \ L \ E \ G \ A \ N \ G \ C \ I \ A \ N \ G \ C \ I \ A \ N \ G \ C \ L \ E \ a \ A \ N \ G \ I \ L \ C \ I \ L \ a \ E \ C \ a \ L \ I$

which is $36$ moves in all.

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

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $253$. -- The Angelica Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $378$. The Angelica Puzzle