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.