I had done the same analysis as Barc and concluded that it's probably the correct answer becauseSpoiler for
As for coming up with a different strategySpoiler forThat said, I bet bonanova's already thought of that and has a solution that still works with those rules despite my argument that attempts to show it's impossible.
plasmid gives me too much credit, so I'm going to out myself now and state that this is adapted from genius puzzler who will be credited when the solution is found. This is done to keep Google out of the competition, not that anyone would do that. Further, I worked on this puzzle until I convinced myself that I could not solve it before looking at the solution. So you guys are the heroes here, not me.
Let me add:
- plasmid's first paragraph makes me wonder. His mirror point seems valid, and it's possible
that my adaptation opened a loophole. If so, a slight modification of the OP avoids it:
The first prisoner solves the puzzle and writes an algorithm on a piece of paper that he leaves in the room.
In that case, and if there are in fact multiple solutions, then Prisoner 1 selects one that they all will use.
In that case, any algorithm that gives AKQ will be a correct solution to the puzzle.
That is, it won't be required that every prisoner would have found the same algorithm (if there are several) and used it.
Or we could say the prisoners are allowed to discuss a strategy beforehand.
- I can provide a helpful clue, one that still leaves a very hard problem, if desired.
Maybe I'm missing something, but I think this might oversimplify the problem. If I can select a specific direction, I think I can get to AKQ in 6 moves from any initial formation, regardless of the time.