Answers 341- THE FLANDERS WHEEL
Move the counters in the following order: AND A F L N 0 A F 0 N L
DRS 0 L N A FRS E R S L N A L-30 moves in all.
[The solution can be reduced to 28 moves, the lowest possible. Readers may
have noticed that the problem is isomorphic with a square, eight-counter
sliding puzzle like the preceding one. For a general discussion of eight-counter
sliding puzzles of this type, see my Scientific American columns for March and
June 1965.-M. G.]
- CATCHING THE PRISONERS
It is impossible for W I (warder) to catch P 2 (prisoner), or for W 2 to
catch P I. In the example we gave it was therefore hopeless, for each warder
1 2 3 4 S (^6 7) B
9 .10 11 J2 n
.
1+ 15 16
@1
Ja
~9
20 '2.1
@~
2;i
(fJ
~5 :u -q 'l8 '2, lc 31 .;J~
33 31-^35 36 ~^16 39 40
would not be chasing "his prisoner," but the other fellow's prisoner. It is a case
of what we call in chess "gaining the opposition." Between W I and P 2 there
is only one square (an odd number), but between W I and P 1 (as also be-
tween W 2 and P 2) there are four squares (an even number). In the second