Seeking Advise from Puzzle Masters

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PadreMontoya
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Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 2:35 am UTC

Hello!

I'm designing a game that features a puzzle that is split into 12 pieces. Once you find all 12 pieces, you can begin to solve it.

The inspiration for the puzzle comes from the classic board game "Mastermind", though there is probably a more technical term for this kind of puzzle. This puzzle also doesn't provide feedback about near-hits; only direct hits.

Players are trying to cure a virus by looking at historical test information to deduce what combination of compounds have 100% effectiveness against the disease. There are <x> amount of compounds, and a compound is only effective if put into the right spot.

Example: The final solution has Oxygen must be in slot #1, Methane must be in slot #2, .... etc.

Clues to the puzzle would look something like this:

Clue #1: L / O / X / M 25% Effective
Clue #2: A / O / B / M 50% Effective
Clue #3: A / X / B / M 25% Effective
Clue #4: A / O / X / M 50% Effective

Hopefully from the above information, you could deduce that A belongs in slot #1 and O belongs in slot #2.

Here's my ask: I'm looking for someone far more clever than I to help design this puzzle properly. I'm concerned about how to balance it so there is only one solution, and that most (or all) of the 12 clues contribute necessary information.

So that's the challenge - is anyone up for it?

Thanks in advance,
- Anthony

Sandor
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Re: Seeking Advise from Puzzle Masters

Postby Sandor » Wed Jun 22, 2016 3:10 pm UTC

There are only a limited number of possible combinations, so I think this should be brute-forceable.

You can try every possible permutation against a set of 12 clues, to see how many match. There should be only one match, obviously. 10 compounds and 4 slots is only 10^4 = 10000 permutations, but I don't think this is enough to need 12 clues.

You can also try every possible permutation against a set of 11 clues, and find out how many permutations fit those clues. If there's only 1 match, then the clue you missed out is redundant. Do that for the 12 sets of 11 clues, and you know if any of the clues are redundant.

You can use similar methods to build up a list of clues in the first place. This method won't tell you how to solve it, just that it is solvable, and that no (or which, if you prefer) clues are redundant.

What constraints are there exactly? I assume you want exactly 12 clues, but is the number of slots fixed? Any constraints on the number of compounds? Or the maximum number and ideal number of redundant clues?

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 3:46 pm UTC

That's clever - I didn't think about programatically generating one.

The main constraints are:

* There must be 12 clues
* It is preferred that every clue matters, but it's fine if some clues provide no useful or new information.
* The answer requires exactly four elements, and the correct elements have to be in the correct slots.
* Each element is only used once within the answer

I'm a decent coder, but I can't wrap my brain around a design pattern for coding a generator for this and testing whether the clues yield useful information and don't lead the players into a trap. I think these types of puzzles are called "process of elimination puzzles"? https://www.google.com/search?q=process+of+elimination+puzzles&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwi49eKB_LvNAhWG2R4KHeDRDg0QsAQITQ&biw=1366&bih=677 Or perhaps it's closer to solving Mastermind. http://puzzling.stackexchange.com/questions/546/clever-ways-to-solve-mastermind

ThemePark
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Re: Seeking Advise from Puzzle Masters

Postby ThemePark » Wed Jun 22, 2016 3:52 pm UTC

But how many elements are there to choose from for a puzzle? You use chemical elements, so can they all be used or is it just the 5 you've used in your example? And can the elements be repeated in a solution?

Your puzzle is exactly like Mastermind, the only difference being the omission of the white pegs, i.e. an element being in the solution but in the wrong place.
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PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 3:59 pm UTC

ThemePark wrote:But how many elements are there to choose from for a puzzle? You use chemical elements, so can they all be used or is it just the 5 you've used in your example? And can the elements be repeated in a solution?

Your puzzle is exactly like Mastermind, the only difference being the omission of the white pegs, i.e. an element being in the solution but in the wrong place.


The answer to that is: I don't know. :) The number of clues and slots are fixed, but I don't know how many elements are needed. Obviously a minimum of 4 are needed, but I don't want to choose an arbitrary number like 8, because it might be too many or two few.

4 of the elements are vital, and the rest are just "noise". There should be enough noise to fill in any slots that don't yield vital information.

ThemePark
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Re: Seeking Advise from Puzzle Masters

Postby ThemePark » Wed Jun 22, 2016 4:16 pm UTC

There's no number of elements that are needed. But the more elements you give the puzzle solver to choose from, the more combinations there are to try out, and the more clues are needed. So you could do this with 4 elements to choose from, or 10, or whatever. And you can make the clues so they give as much information as possible each time, or very little or anywhere in between.

Look at this page I found:

http://mathforum.org/library/drmath/view/70596.html

They mention that the puzzle can be solved in 6 moves at most. And that's with 10 elements to choose from, and 4 needing to be used, and no repeats. I'm not sure if that's for the four or five digit puzzle mentioned though.

But you do need to decide on a number of elements for each puzzle, because the clues must contain all possible elements to choose from. In your example puzzle (which I understand, is incomplete), there are 5 elements, so the solver can only reach a unique solution if there are no more elements to choose from. If Nitrogen was a part of your solution but not anywhere in the clues, there couldn't be a unique solution.

I see now that Sandor also asked about that, i.e. the number of compounds. Anyway, I agree with him, it's easy enough to check a given puzzle for a unique solution the way he described. If you want 12 clues, the absolute maximum elements to choose from would have to be 48, possibly even lower, because then every element would appear exactly once in one of the 12 clues. 49, and there'll be an element never mentioned and thus no unique solution. And with 48 elements in 4 slots and repeats allowed, there'll be 5,308,416 possible solutions for a solver to check using the clues. If repeats are not allowed, it's 4,669,920 possible solutions. So it's definitely doable to check your puzzles for unique solutions.
I have traveled from 1979 to be a member of the unofficial board Council of Elders. Phear M3

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 4:31 pm UTC

Ok, this is starting to make sense!

I think I just need to start off by designing a bare minimum puzzle with perfect information. Example:

Code: Select all

#1: A / ? / ? / ?    25%
#2: ? / B / ? / ?    25%
#3: ? / ? / C / ?    25%
#4: ? / ? / ? / D    25%

As long as all other clues yield 0%, then the right answer is obvious. (A/B/C/D)

From this baseline, it's just a matter of obscuring the answer with clues that don't give conflicting information. i.e.:

Obscuration iteration #1:

Code: Select all

#1: A / ? / ? / ?    25%
#2: ? / B / ? / ?    25%
#3: ? / ? / C / ?    25%
#4: ? / ? / ? / D    25%
#5: ? / A / ? / D    25%


Clue #5 yields information, but it's redundant.

Obscuration iteration #2:

Code: Select all

#1: A / ? / ? / B    25%
#2: ? / B / ? / ?    25%
#3: ? / ? / C / B    25%
#4: ? / ? / ? / D    25%
#5: ? / A / ? / D    25%


The new information about "B" added to #1 and #3 is redundant, since B is clearly solved in #2.

I think I've got this now! Thanks a ton for the discussion. I'll generate a full puzzle later tonight and post it here just for fun. :)

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 4:46 pm UTC

That was actually easier than expected. I'm pretty sure this is solvable.

Code: Select all

Clue #1 : D / C / G / F     Effectiveness: 0%
Clue #2 : A / I / E / J     Effectiveness: 25%
Clue #3 : I / D / C / H     Effectiveness: 50%
Clue #4 : D / A / F / I     Effectiveness: 0%
Clue #5 : C / B / E / D     Effectiveness: 25%
Clue #6 : E / D / B / H     Effectiveness: 25%
Clue #7 : F / G / I / B     Effectiveness: 25%
Clue #8 : I / C / G / E     Effectiveness: 25%
Clue #9 : B / A / D / A     Effectiveness: 0%
Clue #10: E / F / H / J     Effectiveness: 0%
Clue #11: G / I / A / B     Effectiveness: 25%
Clue #12: F / E / B / C     Effectiveness: 0%


Can anyone determine the 4 letter code? Elements range from A to J.

Update: I'm trying to solve this and all of the noise is making it very hard. I might have to revise it to only use 4 elements.

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 5:06 pm UTC

Final Update:

I created a new puzzle and got the result I wanted:

Code: Select all

Clue #1 : B / C / A / D     Effectiveness: 50%
Clue #2 : B / D / A / C     Effectiveness: 0%
Clue #3 : D / A / C / B     Effectiveness: 0%
Clue #4 : D / C / B / A     Effectiveness: 50%
Clue #5 : C / B / A / D     Effectiveness: 25%
Clue #6 : C / A / D / B     Effectiveness: 0%
Clue #7 : A / D / C / B     Effectiveness: 25%
Clue #8 : D / A / B / C     Effectiveness: 25%
Clue #9 : B / C / A / D     Effectiveness: 50%
Clue #10: C / D / B / A     Effectiveness: 25%
Clue #11: C / B / A / D     Effectiveness: 25%
Clue #12: B / A / C / D     Effectiveness: 25%


It only uses 4 elements, so perhaps I'll change the puzzle to be "DNA" instead of periodic elements.

I was able to solve this puzzle within a minute, which is perfect. This puzzle is going to be used in an Escape Room https://www.google.com/search?q=escape+room&oq=escape+room&aqs=chrome..69i57j69i60l3j69i59.1298j0j1&sourceid=chrome&ie=UTF-8#q=what+is+an+escape+room, so I want it to be easy to figure out once I give them some tips about how to build a grid and go through a process of elimination.

Thanks for all of the tips everyone! BTW, who can solve it first? :)

ThemePark
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Re: Seeking Advise from Puzzle Masters

Postby ThemePark » Wed Jun 22, 2016 5:15 pm UTC

Funny that you mention that it's for a room escape game for I have played those for years and years. I'd say that the first one is better suited, even for a room escape game because there's more noise in the second puzzle.

I'm assuming that there are no repeating elements, which you didn't state, but under that assumption, the second puzzle can be solved just from the three 0% effectiveness clues, making the rest of them unnecessary.

Oh, and that solution is
Spoiler:
ACBD
I haven't looked at the other one yet.
I have traveled from 1979 to be a member of the unofficial board Council of Elders. Phear M3

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Wed Jun 22, 2016 5:26 pm UTC

I think by the time the players get all 12 pieces of the puzzle, they aren't going to have much time left. This particular room is not for hard-core gamers, so I want to keep it simple. My goal is for them to feel smart, not actually be smart. :)

I might twerk this one up to have a few more elements and make it a tiny bit more difficult. Once I eliminated possibilities using the 0% information, it only took 5 seconds to figure out the answer. I also noticed that two of the clues were identical.

If you're in the Dallas Texas area, I hope you'll come by when we launch!

ThemePark
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Re: Seeking Advise from Puzzle Masters

Postby ThemePark » Wed Jun 22, 2016 5:35 pm UTC

Århus, Denmark, as it says on the right. I thought you were talking about an online room escape game, which I have played tons of, not a physical one. We have those here too, but they're for groups, and I sadly don't know anyone who cares about that. So I'll keep playing them online. :D

But I would suggest getting some friends to playtest the room, including the puzzle, so they can tell you if it's too hard or too easy or just right, and if time is an issue. Though I like the idea of using the DNA markers if you only want 4 elements to choose from. You could make more slots to make a longer DNA sequence, and because that would allow for repeats, it would make the puzzle more difficult. And the DNA sequence could be a code you'd then have to solve to lead to something else.

Sorry, but I too dabble in puzzles, so I can't help be inspired. :D
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Sizik
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Re: Seeking Advise from Puzzle Masters

Postby Sizik » Wed Jun 22, 2016 5:49 pm UTC

With DNA sequences, you could obscure the clues a bit more by only specifying one half of each pair.
For example, if the solution is

Code: Select all

---------
 A G T C
 T C A G
---------


A 25% clue could look like

Code: Select all

---------
 C     G
   T A 
---------
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Gwydion
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Re: Seeking Advise from Puzzle Masters

Postby Gwydion » Thu Jun 23, 2016 1:28 pm UTC

If you assume that the four elements/bases are not repeated, you can also solve yours with just clues 1 and 2. I guess it depends whether or not you want players to need all 12 to solve (which will make the puzzle take a lot longer too). In my experience with escape rooms, unless you get lucky and fall into a solution, you need to solve everything to move on, and more importantly it feels disappointing when you don't. On the other hand, gathering up 12 things and finding out you only needed 2 of them can also be frustrating.

Do there have to be 12 clues? Can you make 6 and repeat each twice? That would also dovetail with the above suggestion of using incomplete DNA sequences - have 6 incomplete sequences, and their 6 complements. That way, people with some knowledge about DNA and how it is paired get a slight advantage maybe, but even someone with no biology knowledge can have enough information to solve.

For added fun, tell them this is a novel relative of DNA with bases W X Y and Z (or whatever) but that you aren't sure which ones pair with which. That way at least some of the complement sequences are necessary too - now, you can have a puzzle where maybe not all 12 will be necessary for experienced puzzlers, it's relatively easy once you have all the clues, but you can't solve without most of them.

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Thu Jun 23, 2016 3:10 pm UTC

Gwydion wrote:If you assume that the four elements/bases are not repeated, you can also solve yours with just clues 1 and 2.


Great catch Gwydion!

At first I thought this was bad, but here's my new thinking:

* As long as Clue #1 and Clue #9 come out last, it shouldn't be solvable too quickly.

* It can be solved multiple ways, which is good.

* If the group isn't clever enough to solve it the fast way, a clue can suggest they can "brute force" it like I did by drawing 4 x 4 grid of letters.

Code: Select all

1 2 3 4
=======
A A A A
B B B B
C C C C
D D D D
=======


You can then cycle through all of the 0% results and erase letters. That leaves you with a simple set of results:

Code: Select all

1 2 3 4
=======
A     A
    B 
  C   
      D
=======


From there the answer is obvious.

I've done about 5 escape rooms so far with random strangers. Most of the players wouldn't be able to solve a complex puzzle. They are good at finding clues and seeing basic patterns, but there's never been really brain-bending puzzles. (And we've still failed sometimes)

This one feels intimidating at first, but then it's really simple once you realize what to do. There's not any critical thinking involved, but there's the illusion of critical thinking and solving something complex.

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Thu Jun 23, 2016 3:14 pm UTC

BTW, I'm not married to 12 clues. If someone can design puzzle with fewer clues that makes all clues a requirement, I'd be all ears.

Attached is the spreadsheet I'm using to build them.
Attachments
Book7.xlsx
(14.56 KiB) Downloaded 47 times

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Gwydion
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Re: Seeking Advise from Puzzle Masters

Postby Gwydion » Thu Jun 23, 2016 9:17 pm UTC

Here's one option with 5 clues, all of which appear necessary for a unique solution
Spoiler:
ABCD
BAED - 25
BACD - 50
DDAA - 0
CCCC - 25
ABEA - 50

None of the clues individually give away much information, and this can be logically worked through in a couple minutes.

Edit: looking back, the first or fourth clues aren't necessary if you have the other four.

PadreMontoya
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Re: Seeking Advise from Puzzle Masters

Postby PadreMontoya » Thu Jun 23, 2016 9:35 pm UTC

Gwydion wrote:Here's one option with 5 clues, all of which appear necessary for a unique solution
Spoiler:
ABCD
BAED - 25
BACD - 50
DDAA - 0
CCCC - 25
ABEA - 50

None of the clues individually give away much information, and this can be logically worked through in a couple minutes.

Edit: looking back, the first clue isn't actually necessary if you have the other four. It should be easy enough to modify those four clues to make a fifth necessary, if you want.


So that took me about 5 minutes to solve and took quite a bit of thinking. (The first clue was actually the most important to me. Once I determined that
Spoiler:
D
was last, it helped rule out a bunch of positions)

This is cool. Thanks for putting it together. Maybe I'll have an "easy" version and a "hard" version.

ThemePark
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Re: Seeking Advise from Puzzle Masters

Postby ThemePark » Fri Jun 24, 2016 1:14 am UTC

As for your first puzzle, it IS possible to solve, however there is an error. Clue #9 has A twice, indicating that repetition is allowed. However, making the assumption that it is not, it can be solved.
Spoiler:
First off, of course all letters from the 0% clues are removed from all the clues at those positions. Which leaves this:

Code: Select all

Clue #2 : A / I / E /       Effectiveness: 25%
Clue #3 : I / D / C / H     Effectiveness: 50%
Clue #5 : C / B / E / D     Effectiveness: 25%
Clue #6 :   / D /   / H     Effectiveness: 25%
Clue #7 :   / G / I / B     Effectiveness: 25%
Clue #8 : I /   /   / E     Effectiveness: 25%
Clue #11: G / I / A / B     Effectiveness: 25%

So one way to solve this is to look at Clue #6 and make the assumption that H is in fourth position of the solution. Thus all other options are removed from the clues, meaning the E in Clue #8 is removed, and I has to be in the first position and all other letters are removed from that position. Because of the no repetition assumption, that removes the Is from second position, leaving me with this.

Code: Select all

Clue #2 :   /   / E /       Effectiveness: 25%
Clue #5 :   / B / E /       Effectiveness: 25%
Clue #7 :   / G / I /       Effectiveness: 25%
Clue #11:   /   / A /       Effectiveness: 25%

I??H

So E and A both have to be in third position, which they obviously can't, leading me to the realization that H can't be in fourth position. So for Clue #6, D must be in the second position. And the clues look like this now.

Code: Select all

Clue #2 : A /   / E /       Effectiveness: 25%
Clue #3 : I /   / C /       Effectiveness: 25%
Clue #5 : C /   / E /       Effectiveness: 25%
Clue #7 :   /   / I / B     Effectiveness: 25%
Clue #8 : I /   /   / E     Effectiveness: 25%
Clue #11: G /   / A / B     Effectiveness: 25%

?D??

So now I assume the C in Clue #5 is correct. That means the E can't be, and also that no other letters can be in first position. This removes both A and E for clue #2, so the C in Clue #5 can't be correct. So it must be the E. Now I have this:

Code: Select all

Clue #3 : I /   /   /       Effectiveness: 25%
Clue #7 :   /   /   / B     Effectiveness: 25%
Clue #8 : I /   /   /       Effectiveness: 25%
Clue #11: G /   /   / B     Effectiveness: 25%

?DE?

So from Clue #3 and Clue #7, I can see that the last two letters are I and B, making the solution IDEB.
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Tirear
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Re: Seeking Advise from Puzzle Masters

Postby Tirear » Fri Jun 24, 2016 12:57 pm UTC

ThemePark wrote:As for your first puzzle, it IS possible to solve, however there is an error. Clue #9 has A twice, indicating that repetition is allowed. However, making the assumption that it is not, it can be solved.

I reached the same answer without making that assumption, and didn't even need two of the clues. Do you have an example solution that would work with duplicates?

EDIT: Here are my work notes. I might come back and translate to English later.
Spoiler:
3:idch 1/2 6:edbh 1/4 .: one of d2 h4, one of i1 c3 8:icge 1/4 1:dcgf 0 : i1 OR d2 c3 e4 7:fgib 1/4 12:febc 0 .: i1 AND (d2 or h4)
11:giab 1/4 2:aiej 1/4 5:cbed 1/4 10:efhj 0 ... 2 + 10 = i2 or e3, if i2 then h4 then 5:contradiction .: e3 + 11 = b4 .: d2
ans::ideb
use 1235678ABC

Cauchy
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Re: Seeking Advise from Puzzle Masters

Postby Cauchy » Fri Jun 24, 2016 11:49 pm UTC

Gwydion wrote:Here's one option with 5 clues, all of which appear necessary for a unique solution
Spoiler:
ABCD
BAED - 25
BACD - 50
DDAA - 0
CCCC - 25
ABEA - 50

None of the clues individually give away much information, and this can be logically worked through in a couple minutes.

Edit: looking back, the first or fourth clues aren't necessary if you have the other four.


The second and fifth clues here are really strong together: since they don't have any letters in the same positions, we know that two positions from the second clue and two different positions from the fifth clue are correct, so the only possibilities are BAEA, BBCA, BBED, AACA, AAED, and ABCD. The third clue forces the fourth position to be D, and the first and fourth clues each force the third position to be C, after which you've got it.

What I'd say is that if you're looking to make the puzzle easier, have more clues with higher numbers, whereas if you're looking to make the puzzle harder (and require more clues), have more clues with lower numbers. Just one 50% clue cuts down the possibility space a whole lot. If we're looking at your DNA idea with four choices in each of four positions, then for a given sequence, 1/256 match it 100%, 12/256 match it 75%, 54/256 match it 50%, 108/256 match it 25%, and 81/256 match it 0%. If we look at your original proposal, with 10 elements to choose from, then the breakdown for 100%/75%/50%/25%/0% is 1/36/486/2916/6561 out of 10000 sequences. A single 50% sequence here reduces the possibility space by a factor of over 20.

So in short, clues that have a high match rate give away a lot more information than you might have thought.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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