Henry Ernest Dudeney/Modern Puzzles/150 - Counter Solitaire/Solution

From ProofWiki
Jump to navigation Jump to search

Modern Puzzles by Henry Ernest Dudeney: $150$

Counter Solitaire
The puzzle is to remove all but one counter by a succession of leaps.
A counter can leap over another adjoining it to the next square beyond, if vacant,
and in making the leap you remove the one jumped over.
But no leap may be made in a diagonal direction.
Dudeney-Modern-Puzzles-150.png
The following is a solution in eight moves:
$5 - 13$, $(6 - 14, 6 - 5)$, $16 - 15$, $(3 - 13, 3 - 6)$, $2 - 10$, $(8 - 7, 8 - 16, 8 - 3)$, $(1 - 9, 1 - 2, 1 - 8)$, $(4 - 12, 4 - 1)$
This means that $5$ leaps over $13$ and $13$ is removed, then $6$ leaps over $14$ and $14$ is removed, and so on.
The leaps within a bracket count as one move, because the leaps are made with the same counter in succession.
It will be seen that No. $4$ makes the last leap.
Now try to find a solution, in seven moves, in which No. $1$ makes the last leap.


Solution

Play as follows:

$2 - 10$
$4 - 12$
$6 - 5$
$3 - 6$
$7 - 15$
$8 - 16 - 7 - 14 - 3$
$1 - 9 - 2 - 11 - 8 - 13 - 4$


Sources