agaricus5
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Edit:

Please refer to this thread for the puzzle.

This version was rather outdated, so I've removed it to reduce the risk of confusion.

[Edited by agaricus5 at Local Time:11-14-2004 at 06:50 PM]

[Edited by agaricus5 at Local Time:11-14-2004 at 10:48 PM]

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[Last edited by agaricus5 at 10-03-2006 09:22 PM]

Scott
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Do checkpoints count?
Do stairs?
Is a full square of tar the same as a square of tar with a rounded edge?

[Edited by Scott on 03-29-2003 at 02:39 AM GMT]

Scott
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I think this is beyond me. The combinations are just astronomical. I tried just 2 items a wall and an orb and came up with 370 but I am not sure if this is correct. When you start to add in things like roaches with 8 directions the numbers get out of hand.

Schik
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Okay... I came up with a number. Though I tried to be thorough, I can\'t imagine that I didn\'t miss some possibilities. Perhaps I even invented some possiblities, so it will all even out.



If I\'m even remotely close I can try to explain my logic.




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eytanz
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This is very, very complicated. The stackable items alone make this a lot of work - but what about items like snakes (snake components must be connected in a sensible fashion; you can\'t have unconnected/unaligned snake body parts), beethro and his sword (must be positioned in a certain way relative to each other), the \'neather and his mallet (ditto), and, worse of all, mimics (can a mimic exist in a dungeon that has no beethro in it? can two mimics exist that face different directions)? And is it ok to have a mimic or beethro facing so that their sword is out of the room?

And what about blue doors? There can only be one blue door in a level; does that mean that there can\'t be two seperate ones in a room? Can a closed red, blue or green door square exist in a room that also has an open one of the same color?

Similarly, for tar - a square of tar cannot exist seperate from other squares. In fact, there is only one possible tar combination that can exist in a 2x2 room. But a 2x2 subset of a larger room can have other tar shapes. So which is it in this case?

So, the main question is - are we supposed to find all combos legal *in* a 2x2 room? or all legal combos that take 2x2 squares? or even illegal combos?

These questions are what makes the question really complicated; otherwise it\'s just a matter of counting possible types and combinations and doing some combinatorics.

---

oh... And I think for just two items the answer is 81, not 370 (3 states for each square - wall, orb, or empty; 3x3x3x3 combinations).

Eytan

(edited as I think of more complexities)

[Edited by eytanz on 03-29-2003 at 03:27 AM GMT]

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Scott
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Well I did say it was beyond me

morals
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that would be 4 raised to the power of # of possible elements, which is indeed a very huge number

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zex20913
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No...I think it would be the number of possible elements raised to the power of 4. That may be an even LARGER number.

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levelthirteen
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zex20913 wrote:
No...I think it would be the number of possible elements raised to the power of 4. That may be an even LARGER number.

I would phrase it as the total number of different tiles ^4; a tile including monsters, gates, etc. plus multi-tile possibilities such as serpents. This is much smaller then 4^(# of tiles).
5^4 = 625, 4^5 = 1024
10^4 = 10000, 4^10 = 1048576

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morals
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zex20913 wrote:
No...I think it would be the number of possible elements raised to the power of 4. That may be an even LARGER number.

oops, that\'s true well, it\'s an obscen number as well fortunatelly not that obscene as before

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agaricus5
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Keep going all of you: you are all on the right track. In response to earlier questions, it is the number of legal combinations of a 2x2 room (for example, no lone tar corners or sides) that I\'m looking for. I did not wish to include the \'Neather, Mimics or Beethro yet (It will be part of the third part of this puzzle) and stairs and checkpoints are certainly not included yet.

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agaricus5
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zex20913 wrote:
No...I think it would be the number of possible elements raised to the power of 4. That may be an even LARGER number.

Unfortunately, it\'s even bigger than that...I\'m sorry.

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krammer
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A list of every possible type of square:

Floor
Wall
Crumbly wall
Pit
Trapdoor
8 types of arrow
Yellow door (open)
Yellow door (closed)
Red door
Green door
Blue door
Orbs
Mimic potion
Invisibility potion

Now to things on squares. The following have 8 orientations:
Roach
Queen
Wraith
Evil eye
Goblin

With only one orientation:
Tar baby
Spider
Brain

All of the above can fit onto trapdoors, floor, open and closed yellow gates, arrows - that is 12 possibilities per monster. Wraiths can also fit on pits.

There are 43 monster/person types excluding serpents, tar and mothers. This makes a total of 545 different types of square.

I can\'t seem to get any further - but maybe that helps someone else.

I excluded snakes as they are very complicated, and tar and mothers as there are only 3 possible combinations for those.
Unless - does tar on walls count as a different square to tar on floor?

Edited because I made a stupid mistake

[Edited by krammer on 03-29-2003 at 09:19 PM GMT]

[Edited by krammer on 03-30-2003 at 06:27 PM GMT]

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agaricus5
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Tar on pits? Can you get that in DROD?

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zex20913
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Wow...I feel silly. I forgot to take into consideration the possibilities of certain things...whatever it is, I now think the total number is, excluding snakes, the total number of combinations that can be made in one square (monster;monster&floor type/floor object {arrow}) to the sixtieth power, plus 2. (empty entirely, and tar bubble. Wraithwings over pits are included in the thing to the sixtieth.) If we go with the *in a 2x2 room* rule recently put across, we only have to add 24 for the snakes...then multiply that by possible floor combos...Wesley...do ALL rules still apply to this puzzle, such as *snakes can\'t go on force arrows*? Even if this does not hold true, it should be a lot closer than my previous guess of whatever to the fourth. BTW...it IS possible for the number to be as I said, larger.

2^3=8, 3^2=9.
3^4=81, 4^3=64.

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agaricus5
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krammer wrote:
I can\'t seem to get any further - but maybe that helps someone else.

Yup. It certainly helped me, but it\'s going to infuriate everyone else:

The solution is now at least 5 times bigger (I calculated it just now)

Oh dear!

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agaricus5
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zex20913 wrote:
Wesley...do ALL rules still apply to this puzzle, such as *snakes can\'t go on force arrows*?

Yes: all rules have to apply (the recearchers have done some studying into dungeon inhabitants from various sources and so do know things like the fact that serpents cannot go on force arrows).

[Edited by agaricus5 on 03-29-2003 at 10:18 PM GMT]

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zex20913
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What about scrolls?

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agaricus5
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I found this bug on Level 7 while looking for solutions for my puzzle, and so have included it as part of the solution to the puzzle:

Serpents cannot go on scrolls.

Go to Level 7 1N - 07(00,01) and stand on the scroll, and wait. You\'ll see what I mean.

(I have also posted this on the Bugs section)

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krammer
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agaricus5 wrote:
Tar on pits? Can you get that in DROD?

Oops. I meant tar on walls.
This is what comes of trying to do this kind of thing too late at night.

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agaricus5
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Oh...I just remembered. This refers to Caravel DROD 1.5, so the solution doesn\'t include floating scrolls.

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agaricus5
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I announce...the solution is bigger...













by 1!

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Mister
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Krammer said 545 different types of square, but I count 546... (can brains exist on doors?)

There are 21 \"terrains\", 12 of them accept monsters normally; 43 types of monsters; and nine special cases (Baby on Wall, Wraiths on Pits).

9+12*44+9 = 546 (excluding tar, mothers, serpents, savepoints and scrolls)

BUT, only a single blue door can exist, and there are only two configurations of non-adyacent blue doors.

Considering this, the total seems to be:


Now, to add serpents to the equation...
Serpents can exists on Floor, Trapdoors and Yellow doors (four types of squares only).

A maximum of two serpents can exist on so little room.
Two serpents fill the room, in 8 different configurations. This adds 4^4*8 combinations.
One serpent, four squares length: 8 possibilities. This adds 4^4*8 combinations.
One serpent, three squares length: 8 possibilities. This adds 4^3*8*546 combinations.
One serpent, two squares length: 8 possibilities. This adds 4^2*8*546^2 combinations.

And the total is (excluding tar, mothers, savepoints and scrolls):



But the problem is for all legal starting combinations? If so, are monsters allowed over closed doors?

agaricus5
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mister wrote:
Krammer said 545 different types of square, but I count 546... (can brains exist on doors?)

Careful... This is part of the speculation zone.
I think that they should exist though.

There are 21 \"terrains\", 12 of them accept monsters normally; 43 types of monsters; and nine special cases (Baby on Wall, Wraiths on Pits).

9+12*44+9 = 546 (excluding tar, mothers, serpents, savepoints and scrolls)

Oh you...


The solution is now at least a few tens of thousands bigger. (Checkpoints not included because Dugan\'s recearchers never discovered such high technology - I\'m sorry)

BUT, only a single blue door can exist, and there are only two configurations of non-adyacent blue doors.

Nope.

On Level 21, there are 4 separate blue doors.

And the total is (excluding tar, mothers, savepoints and scrolls):

Click here to view the secret text

×101184468984 + 38442496 = 101222911480

But the problem is for all legal starting combinations? If so, are monsters allowed over closed doors?

All legal combinations are incorporated into the solution (Monsters do not get squashed on closed doors, in the game and on the open field where the experiment takes place)

You are getting close to the answer, but it\'s not quite there yet. However, keep going...the systematic approach you are using is the one I used myself.

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levelthirteen
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Can scrolls be on force arrows, pits, open door tiles, under a green door, under a blue door, or under/on top of a crumbly wall? And can force arrows be on open door squares?

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Canthlian
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In Caravel DROD, scrolls can\'t be on pits. They fall down. (This was changed from the original DROD. There\'s a room somewhere that demonstrates this, I think) And I\'m pretty open doors and force arrows don\'t mix.

Mister
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Uh, oh... there are far more combinations than I calculated: I forgot arrows on trapdoors! (as in Floor 23,1S,3W)

Ok, I\'ve compiled what\'s posible and what isn\'t. Feel free to point out any mistakes and to fill out the \"?\".

              Roach Queen Wraith Eye Goblin Spider Brain Serpent Tar Mother Baby
Floor           Y     Y     Y     Y     Y     Y      Y      Y     Y    Y     Y
Checkpoint      Y     Y     Y     Y     Y     Y      ?      Y     Y    ?     Y
Scroll          Y     Y     Y     Y     Y     Y      ?            ?    ?     Y
Scroll/Trap     Y     Y     Y     Y     Y     Y      ?            ?    ?     Y
Trapdoor        Y     Y     Y     Y     Y     Y      ?      Y     Y    Y     Y
Arrow           Y     Y     Y     Y     Y     Y      ?                       Y
Arrow/Trap      Y     Y     Y     Y     Y     Y      ?                       Y
Yellow Open     Y     Y     Y     Y     Y     Y      ?      Y     Y    ?     Y
Yellow Closed   Y     Y     Y     Y     Y     Y      ?      Y     Y    ?     Y
Wall                                                              Y          Y
Pit                         Y
Crumbly Wall                                                      ?    ?     ?
Red door                                                          ?    ?     ?
Green door                                                        ?    ?     ?
Blue door                                                         ?    ?     ?
Orbs          
Mimic potion
Invis potion

Total combinations for a single square (without considering questions marks nor serpents): 1016!!!

[Edited by Mister on 04-06-2003 at 03:46 AM GMT]

eytanz
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You need to split red/green/blue doors to open/closed states as well.

Any monsters that can be on an open yellow door can be on an open red door.

Also, tar babies can be on open green and blue doors. If there\'s tar in the room, you can first clear the room to open the green/blue door, and then create a new tar babies by cutting through the tar, which could go on the open door square.

Any reason why tar mother on walls is not a question mark? We never see one in the game, but how do we know it\'s impossible? Same for tar/mothers on arrows.



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Mister
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red/green/blue doors, when opened, just disappear, that\'s why I didn\'t count them

Any reason why tar mother on walls is not a question mark? We never see one in the game, but how do we know it\'s impossible? Same for tar/mothers on arrows.

True... Really, we need a developer to answer this for us, as we don\'t know even about serpents on arrows, for example.

eytanz
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mister wrote:
red/green/blue doors, when opened, just disappear, that\'s why I didn\'t count them

Oh yeah, of course. D\'oh.

[Edited by eytanz on 04-06-2003 at 03:50 AM GMT]

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