TRAFFIC JAM PUZZLE
Two groups of 5 people are crossing a river in opposite directions by hopping on rocks. There are eleven rocks (numbered 1 - 11) and in the starting configuration, the empty rock is in between the two groups:
> > > > > < < < < < ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 2 3 4 5 6 7 8 9 10 11
GOAL:
The objective is for the two groups to exchange sides, that is, to pass each other. Thus, the winning configuration is:
< < < < < > > > > > ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 2 3 4 5 6 7 8 9 10 11
RULES:
1. You can only move forward in the direction you are facing. No backstepping or turning around.
2. Only one person may move at a time.
3. There are two kinds of legal moves:
EXAMPLES:
> > > > < > < < < < ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 2 3 4 5 6 7 8 9 10 11
3 or 6 can move.
> > > > < > < < < < ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 2 3 4 5 6 7 8 9 10 11
4 or 8 can move.
> > > > < < < < < > ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 2 3 4 5 6 7 8 9 10 11
None can move.