|
The
Game of Five
|
Strategies
and Hints
-
The arrangement 31524 can be transformed into 15243, 52431, 24315, or 43152 by moving the tiles in a clockwise direction.
-
One arrangement can be transformed into another only if they are both even or both odd. It is impossible to transform an even arrangement into an odd, or the reverse. Students might convince themselves that this is true by trying different arrangements of a set of digits and noticing that the parity (evenness or oddness) of the arrangement is always preserved.
-
Any odd arrangement; for example, 12354, cannot be changed into the even arrangement 12345.
Solution
There are 5! = 120 possible arrangements. Half of these are even and
half are odd. The solution to the specific problem can be accomplished
in 36 moves, 5 of which are not clockwise rotations: 14352 
31524 41532
21543 42351
12345
 |