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

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

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.

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?

1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Moving Counter Problems: $246$. -- Transferring the Counters
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Moving Counter Puzzles: $372$. Transferring the Counters