# Find your way to the control room

You are a space explorer, who accidentally finds an alien spaceship which seems to be deserted. You, and your team want to get to the control room, but you understand aliens and their technology only partially, so you have to experiment along the way.

When you entered through a hole in the ship's stern, there were no doors or passages. However, there was something eerily similar to what people call transportation pod, and its control panel looked roughly like the following diagram made by one of members of your team:

Of course, the aliens didn't use letters, that just convenience for us, humans. The blue dot denotes the ship's stern room and the red is the room marked with alien pictogram for control room. The yellow and green orbs are buttons.

You didn't know if it would work, but being an adventurous person, you dared to try. You pressed button D▲ and the pod, together with your team moved to room 1, with a small light on the panel acknowledging your new current position.

Well, maybe it does work? You press R▲, but contrary to your expectations, you move to room 2, instead of 3. Now, that's strange, isn't it?

Perhaps, you should've press the R▼ button instead? You do, and indeed the pod moves to room 3. But then, to test your theory, you press B▼ and end up in room 4.

What is going on? Can you find your way (a sequence of button presses) to the control room (you start in room 4)?

Hints for movement mechanics:

• If you are in room B, pressing button Q▲ moves you to the very bow of the ship, while pressing Q▼ moves the pod to room S.

• If you are in room A, pressing any of the (P,Q,R,S)▼ will take you also to S, and not stern, which also could also seem like a possibility.

• In particular, pressing P▼ from room A won't take you to the control room, because you cannot reach it from P going only downwards.

Some clarifications:

• You start in room 4, but if you want to start at stern, that's alright too (in case it is not obvious, pressing D▼ in room 4 will get you to the stern).
• Vertical lines are valid as any other lines.
• It seems that my story is not revealing or constraining enough, so if you are confused, please use hints. My intention was for you to have fun, not get frustrated by an insufficiently described puzzle mechanics.

Edit:

By mistake I've uploaded wrong version of the picture (I have to use several iterations to construct a puzzle). There is small "bridge" which significantly changes the problem (now a solution exists). Sorry for that $\ddot\frown$

• Nice puzzle. Does the solution have to be a sequence which gets you to the control room from the stern? (Or from any position?) Is there a "reset" which brings you back to the stern? *Might be something to add to your puzzle to clear up the story line? Otherwise one would now seek a way from room-4 to the control room...) – BmyGuest Sep 20 '16 at 10:49
• Does the story, as it is, (without the hint) provide enought information to find and verify the correct solution? It seems to be a little sparse on information, but I have not worked on it hard yet. – BmyGuest Sep 20 '16 at 10:52
• @BmyGuest Indeed, you start in room 4. And, there is a sequence of buttons that could get you back to stern. – dtldarek Sep 20 '16 at 11:01
• @BmyGuest Technically no, because the buttons could do just anything (there are no constrains, right?). Practically yes, because there is a nice general way the buttons work, and if you find that, you will immediately know that it is the correct thing (at least I hope so, and I will edit the puzzle to make that true if it isn't true now). – dtldarek Sep 20 '16 at 11:04

My guess is that the control panel represents a

Lattice. The Buttons represent the supremum/infimum of your current location with the location of the button.

Example:
If you are standing in room 4 and press C▲ it would take you to the supremum of room 4 and C which would be the next junction to the top and right of C.

The control room can not be reached. To enter the control room you would have to enter from the top right (and press A▼). But none of those junctions are possible to reach because all the possible combinations to reach them have supremas below the junctions.

Solution after edit:

The control room can be reached from room 4 by pressing the following buttons: R▲C▲P▼Q▲D▲A▼

Image of solution C▲R▲P▼Q▲D▲A▼ (because it is easier to draw):

• Hello and welcome to Puzzling.SE. Please consider registering. Also, could you kind of explain how do the buttons and the up/down arrows are related to your solution? I am familiar with the lattice concept, and the supremum/infinum you talk about, but kind of get lots halfway. Please add some details. – Matsmath Sep 20 '16 at 12:21
• First part is almost right (see the hints, it cannot be a pure lattice). Second part is wrong (I've rechecked the solution again, and I think it works). – dtldarek Sep 20 '16 at 12:21
• @dtldarek I can not see how any of the hints conflict with my guess. – w l Sep 20 '16 at 12:31
• @user30265 You were right, by mistake I've uploaded wrong picture, there was no solution. (It's fixed now.) – dtldarek Sep 20 '16 at 12:49
• @Joe Try to think about floors. If a room is on the same horizontal line as another room, they are on the same floor. If it is lower, it is on a lower floor. Every junction represents a room. Now pressing the ▼ button will check all rooms that can be reached from both points by only moving to rooms at a lower floor and out of those pick the room on the highest floor. While R is also reachable from both points, the room just above R is on a higher floor and thus chosen. – w l Sep 20 '16 at 14:46

This is an answer to get the ball rolling. I'm not really expecting to be right, but maybe it helps someone :P

Edit: To clarify, I'm starting from Room 4.

It appears that pressing up or down:

will move you as far as possible towards that button, in an up-ish or down-ish direction, until you either arrive in a named room, or the next directional move would leave you further from your target room than you are now (this explains why R ▲ in room D stops at 2).

To get to the control room, I'd therefore push:

D ▲ (arrive at the intersection of the middle-line from D and the B/S highway as that's the closest to D)
D ▲ (nudges us over one further, onto the control room line. Going any further would take us further away from D)
P ▲ (arrive in control room)

• Yes, you should start from room 4. – dtldarek Sep 20 '16 at 11:05
• @dtldarek since you didn't say my solution is correct, presumably it's wrong? :) – Joe Sep 20 '16 at 11:05
• Pressing R▼ from room A will get you either to S. – dtldarek Sep 20 '16 at 11:10
• Any of the buttons (P,Q,R,S)▼ pressed in room A will get you to room S. – dtldarek Sep 20 '16 at 11:30
• @dtldarek OK, added an important change to my answer, let's see if we're there yet :) – Joe Sep 20 '16 at 11:34

The right sequence might be (starting at blue dot)

A▲, which should leave the pod in room of button A Any button on the right (P,Q,R or S)▼ should let us into the control room (red dot)

or

D▲, P▲, A▲, A▼, any right (PQRS)▼ if the vertical slides are not valid

because

According to your directions, if you press a button ▲, the pod tries to reach that button, but only going more upwards than downwards. If it cannot comply to the upwards rule, it stops. The ▼ buttons work by the same pattern (move closer to the button room but only downwards)

EDIT

Being in room X and pressing the Y▼ button will take you to the point, which is reachable from both X and Y only moving downwards. Pressing Y▲ means the point reachable from X and Y upwards. If you cannot reach the destination (Y), you go the path requiring fewer number of "steps". Reaching the control room could be therefore completed by (starting from the room 4):
Q▲(Q)
R▲(over the bridge)
D▲(3 verticals over room "2")
A▼(into the control room)

• But the first move is D▲and the pod moves downwards – Kirex Sep 20 '16 at 11:14
• Any of the buttons (P,Q,R,S)▼ pressed in room A will get you to room S. – dtldarek Sep 20 '16 at 11:17
• @Kirex - starting at "blue dot" room and pressing D▲ results in going to room D which is upwards – oleslaw Sep 20 '16 at 11:21
• @dtldarek If vertical moves are not allowed (which I believe is the case), (P,Q,R,S)▼ in room A will move us through the middle of the graph (to the "red dot" room). But if the vertical moves are available, the effect could be nondeterministic given only the rules I provided in the answer. – oleslaw Sep 20 '16 at 11:23
• @oleslaw I misread the puzzle, I'm sorry. I'll pay more attention next time. – Kirex Sep 20 '16 at 11:24