bonanova

What is the initial division? 3x3x3? something else? or purposely not given?

If we have enough others willing to play, I am happy to relinquish my spot and watch this one. Still learning the game, and these rules are complex. Is that agreeable?

It would be interesting compete with a list of moves that gets to the "highest" y-value. Earlier solvers disallowing diagonal moves could get only to y=4. I've played with this but it gets complicated too quickly.

Y-San, do your steps have a cycle?

Don't see that it matters. The configuration dictates the move, not the time of day. The solution is not "If it's 3:00 then place the Q on top of the A." With a random warden, Prisoner 1 might make the winning move. Y-San's post tells the nature of the solution, so let's just pose it that way: Arrange the configurations into categories of your choice, then give the correct move for each case.

If a patient is released, can s/he ever be re-committed?

As for coming up with a different strategy That 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.

Nice analysis. You may have made some assumptions you don't need to make. Here are some things to consider.

Can we deduce from this an upper limit on y (for the OP)?

I kept reading this as, what is the index of the first term whose index is equal to 1? Argh. It's what is the index of the first term whose value is equal to 1. So now I ask, is that term 1 or is it 0001? That is are the terms simple numbers? or are they 4-tuples?

Does the sequence end with the 10th character? Or would you rather not say?

Good questions. The prisoner must make a move. Wait. No, he doesn't. But skipping a move only makes it harder to finish by 5:00pm. The move is based solely on visible cards. The move may not be reconsidered based on information gained by making the move. 0. Enter the room. 1. Look at the (visible) cards. 2. Decide which visible card to move and where to move it. 3. Make the move. 4. Leave the room. Re time of day. I introduced time of day only to limit the total number of moves. But you may assume the prisoner has a functioning timepiece. Gratuitous fact: Left, Middle and Right are labels whose only function is to enable a description of what a prisoner might see and what move he should then make.

The warden is at it again. The entire prison population will be set free if the inmates can achieve a simple result. They must stack three cards, an Ace, King and Queen, on a table, in that order, with the Ace on top. Alone and in a closed room, the warden begins the process by placing the three cards face up on a desk in some or all of three bins, appropriately marked Left, Middle, and Right. If they all occupy a single bin, only the top card is visible. If they occupy only two of the bins, then only two cards are visible, and it is impossible to tell which of the two visible cards conceals the third. Of course if they are all in separate bins, all three are visible. How the cards are initially laid out is totally up to the warden, but for the purposes of this puzzle we may assume the placement is random. At 8:00am on the fateful day, a prisoner chosen at random enters the room and moves one of the visible cards from its bin to a different (possibly empty) bin. That is, from the top of one stack to the top of another (possibly empty) stack. The prisoner then leaves the room and is led back to his cell. He does not communicate in any way with the other inmates. Then at 9:00am, and at one-hour intervals thereafter, a second, third, etc., randomly chosen prisoner enters the room and again moves a single card from the top of one pile to the top of another. A prison guard inspects the cards after each move and informs the warden if at any time the three cards become stacked in a single bin in the desired order: Ace, King, Queen, with Ace on top. The cards must be correctly stacked by the time the 5:00pm prisoner leaves the room, or before, for the prisoners to be released. They are all executed otherwise. The prisoners are not permitted to work out a strategy beforehand. In fact, the prisoners do not know what they are expected to do until they enter the room. We could say that prisoners enter the room, read the above description of the problem, make their move, and then leave. What are the prisoners' chances? We can assume they are smart. Smart enough to be Brain Denizens.

RID=Role ID e.g NK barc= you kill barc RID kill Barc as Psychologist= you kill barc if only barc is psychologist (you should know the role of a player you are acting on to succeed, or guess correctly) The idea being that you don't want barc to die if you're wrong about his being the psych?

Confirming. What does RID mean?

A retired gynecologist decided to become an auto mechanic. He was a good student and passed the final exam with flying colors. You are amazing, said the instructor, after the student had rebuilt an engine in record time. You mean no one else was able to rebuild an engine? asked the doctor. Of course, said the instructor, but no one else did it through the tail pipe!

Diagonal adjacency permitted? Only A-Z characters? What does "corners count" mean?

An infinite army of ants comprises soldiers with integer coordinates on the lower half-plane including the x-axis (non-positive values of y.) The army advances upward by jumping over adjacent comrades to unoccupied positions. The y-value of the jumping ant thus increases by 2. The comrade, however, is killed in the process and removed from battle. The effect is like moves in checkers, where the jumped checker is removed, except that the ants may advance vertically as well as diagonally forward. Horizontal jumps are also permitted, but no ant may retreat. To win the war, an ant must reach an enemy stronghold somewhere in the upper half plane. Can the ants advance to arbitrarily large values of y? Example of a jump to the northeast: x ------ x x x x x x x x x x --- x-axis --- x x x x x . x x x x ------- ... x x x x x x x x x x ... ... x x x x . x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ... ... x x x x x x x x x x ...

Does it blow memory to keep a tree structure for each starting number? That's the same storage requirement as a 255x255 matrix.