Quewort
Level: Delver
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Well, I was thinking a lot about it: Is it possible to create so many puzzles in DROD, that next new puzzle will have exactly the same solution as previous ones? I don't mention scripting, though.
I don't know how to get this thought further, but... I'm afraid puzzles aren't endless. Or it depends on our creativity level?

I'm bad at writing, but I guess you got the idea.
The sky's the limit...

RoboBob3000
Level: Smitemaster

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Disregarding software/hardware limitations, if you include scripting, you can make an infinite number of rooms with unique solutions. Imagine a script that waits X turns, then strikes an inaccessible orb to release a roach, making the room solvable. In this case, X can take on an infinite number of values that produce unique solutions.

If we take scripting out of the equation, I believe that there is a finite number of solvable individual rooms with unique solutions. There is a finite number of combinations of elements, orientations, and entrances that a room can consist of, and the set of solvable rooms is a subset of all rooms.

However, you phrased the question using the word "puzzles" instead of "rooms". It is possible to design script-free rooms that have interdependencies between themselves and other rooms with respect to possible entrance/exit locations and player orientations, which can also potentially be chained across several rooms (see KDD Level 24, or Compass Point, or to an even simpler degree, KDD level 13). Because there is no technological limit to the number of rooms in a level or hold, there is no limit to the number of potential chained interdependencies. Thus, there is an infinite number of potential solutions for solvable rooms, if we expand the idea of a solution to include moves that need to be made in interdependent rooms.

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[Last edited by mrimer at 09-30-2015 04:22 PM]

Crimson Moon
Level: Master Delver

Rank Points: 108
Registered: 08-04-2014
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I think with how many different elements we have, it would take a long long time for that to happen, and with every new DROD game, even new elements are added. There are already similar puzzles in DROD, and it's bound to happen again. But there are certain ideas for solving a puzzle that you can make more or less complicated, so although they are similar, they still are solved differently.

Think of it like music. Music eventually is going to run out of possibilities, and if you search hard enough, there are already extremely similar sounding songs.

I don't think we have to worry too much. It's still extremely hard to make an exact carbon copy of someone else's puzzle accidentally. You would pretty much have to know the puzzle and purposely copy it. If it somehow happened, that's what beta testing and submitting the hold is for to avoid having duplicate stuff come out. So if your worried you might accidentally create a puzzle someone else created, then I think you'll be alright and odds are, you won't

Insoluble
Level: Smitemaster

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Quewort wrote:
Well, I was thinking a lot about it: Is it possible to create so many puzzles in DROD, that next new puzzle will have exactly the same solution as previous ones? I don't mention scripting, though.
I don't know how to get this thought further, but... I'm afraid puzzles aren't endless. Or it depends on our creativity level?

I'm bad at writing, but I guess you got the idea.
The sky's the limit...

There is no risk of this ever happening in anyone's lifetime. In theory there is probably an upper bound on the maximum number of moves required to solve a DROD room, which means that the number of distinct move combinations is finite. But that number of move combinations would be so massive as to be unplayable in anyone's lifetime.

On any given turn there are 11 possible moves (well, 12 if you count special command, but it sounds as though you are not counting scripting.) If you wanted to create a different room for each of the different possible solutions that are exactly 50 moves long for instance, there would be about 11^50 of them. This is well over 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 rooms. To put that in perspective, if you live to be 80 years old you will have lived for about 2,500,000,000 seconds. That means that even if you play one room per second, you will only have played the most insignificant fraction of those rooms.

Now I realize there are a couple problems with this approach to counting. It may be difficult to impossible to create an interesting puzzle for many of those 11^50 possible 50 move combinations (waiting 50 turns in a row for instance seems a bit trivial), but given some of the stuff people have come up with already, I have no doubt that interesting puzzles could be created for a good chunk of them. Another problem is that you'd have a difficult time creating a room in which one 50 move combination is a valid solution but no other 50 move combinations are. This would cut down on things a bit, but again, that total number of move combinations is so huge (in this is only for 50 moves which is a pretty low move count) that there is no doubt in my mind that we will continue to see rooms with distinct solutions.

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[Last edited by Insoluble at 09-22-2015 06:28 PM]

skell
Level: Legendary Smitemaster

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I think you are concentrating too much on the letter and not the spirit of the law... Erm, the post.

I think what Quewort means - will we ever run out of puzzles assuming that two very similar puzzles which give the same feel for solution are the same puzzle.

And I think the answer is no. The vast number of interactions in the game and the number of interactions between the interactions... I can't do a mathematical proof but that's what I believe!

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Dischorran
Level: Smitemaster

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That could be an interesting contest, actually. Given a demo in an empty room, design as interesting a room as possible such that the demo clears the room.

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adS
Level: Master Delver

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Registered: 05-02-2010
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It is quit clear that the number of starting positions (no scripting) is finite and it is probably quite easy to estimate an upper bound.

To find a good upper bound for solvable positions is certainly much harder to find.

To the mathematicians: Find an upper bound.

Best wishes,

adS


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pauca sed matura

Someone Else
Level: Smitemaster

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Here's an upper bound: Graham's number.
I can probably do better, but I'll get back to you on that.

adS
Level: Master Delver

Rank Points: 214
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Someone Else wrote:
Here's an upper bound: Graham's number.
I can probably do better, but I'll get back to you on that.

Really? Unfortunately I don't know Ramsey theory.

Anyway, using some very deep theorems from Analytic Number Theory I have established a lower bound:

1

Best wishes,

adS

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pauca sed matura

Banjooie
Level: Smitemaster

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Dischorran wrote:
That could be an interesting contest, actually. Given a demo in an empty room, design as interesting a room as possible such that the demo clears the room.

Okay this idea is amazing, scroll back up and mod it up, guys.