Henry Ernest Dudeney/Puzzles and Curious Problems/246 - Transferring the Counters/Solution

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Puzzles and Curious Problems by Henry Ernest Dudeney: $246$

Transferring the Counters
Place ten counters on the squares of a chessboard as here shown,
and transfer them to the other corner as indicated by the ten crosses.
Dudeney-Puzzles-and-Curious-Problems-246.png
A counter may jump over any counter to the next square beyond, if vacant,
either horizontally or vertically, but not diagonally,
and there are no captures and no simple moves -- only leaps.
Not to waste the reader's time it can be conclusively proved that this is impossible.
You are now asked to add two more counters so that it may be done.
If you place these, say, on $\text {AA}$, they must, in the end, be found in the corresponding positions $\text {BB}$.
Where will you place them?


Solution

Place the extra counters:

one on the fourth square in the second row from the top
one on the second square in the fourth row from the top

thus:

Dudeney-Puzzles-and-Curious-Problems-246-solution.png


Then they may be played as follows:


This theorem requires a proof.
In particular: and so it goes
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Sources

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