Henry Ernest Dudeney/Puzzles and Curious Problems/252 - Black and White/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $252$

Place four light and four dark counters alternately in a row as here shown.

The puzzle is to transfer two contiguous counters to one end and then move two contiguous counters to the vacant space,

and so on until in four such moves they form a continuous line of four dark counters followed by four light ones.

Then try this variant.

The conditions are exactly the same, only in moving a contiguous pair you must make them change sides.

How many moves do you now require?

$(1): \quad$ In the first case, move:

$6 7$ before the $1$, then $3 4$, $7 1$, $4 8$ to the vacant spaces, leaving the order:

$6 \ 4 \ 8 \ 2 \ 7 \ 1 \ 5 \ 3$

$(2): \quad$ In the second case, move:

$3 4$ and replace them as $4 3$ before the $1$, then move and reverse $6 7$, $6 5$, $3 1$, $6 8$ into the vacant spaces, leaving the order:

$4 \ 8 \ 6 \ 2 \ 7 \ 1 \ 3 \ 5$