Testing a riddle for my game - please try to answer

[Jon_Dahl]

EDIT: I have followed Kurald Galain's advice and made the sequence longer.

Hello, everyone! Clerics of Boccob do not want creatures with low IQ visiting their meditation chambers that are open to everyone who wants to mediate (but dumbnuts are not welcome). When someone arrives at the main corridor, a permanent magic mouth AND a text on the wall advise the person to shout the answer to the following question:

"6, 4, 12, 8, 24... what comes next?"

Anyone who enters the corridor without shouting the right answer will face a golem that waits behind a secret door, who mangles the dead and pushes the remains down to small hole.

16. In this two-phase sequence, you first subtract one-third and then multiply the result by three.

[Mr Adventurer]

What's numerological sequences got to do with genius poetry, or art, or skill with the pen? What's it got to do with genius philosophy or with being a savant of magic?

All irrelevant questions compared to: what skills do your players have that they will apply to this puzzle, or, alternatively, do the PCs have the right skills on their character sheets for them to solve this?

[Jon_Dahl]

What's numerological sequences got to do with genius poetry, or art, or skill with the pen? What's it got to do with genius philosophy or with being a savant of magic?

All irrelevant questions compared to: what skills do your players have that they will apply to this puzzle, or, alternatively, do the PCs have the right skills on their character sheets for them to solve this?

They can roll an intelligence check OR try to figure it out, if their characters' intelligence is at least 10.

[Jon_Dahl]

Sorry, the riddle was broken, but it's okay now.

[Kurald Galain]

As every Greyhawkian knows, Boccob's prayer goes like this:

Boccob, Bless Academicianship Knowledge Everywhere.

So that's 6 letters, then 5, then 15, and the next number is 9.

Three numbers is way too short to determine a sequence; I can make up equally-plausible answers for why the next number would be e.g. 12.5 or -85. This is not something people can answer unless they know the answer beforehand, so it's less of a riddle and more of a gotcha.

[VariSami]

While I would have hit on the right answer, what you need to understand is that for each limited sequence, there is an infinite number of rules which correspond to it and for which the next value in the sequence may differ radically.

I would allow the players to use any answer for which they may express a compatible calculation rule instead of insisting that there is just one proper answer.

[Jon_Dahl]

While I would have hit on the right answer, what you need to understand is that for each limited sequence, there is an infinite number of rules which correspond to it and for which the next value in the sequence may differ radically.

I would allow the players to use any answer for which they may express a compatible calculation rule instead of insisting that there is just one proper answer.

Agreed. If they give another answer, I want to see the calculation rule and if it's sensible, I will allow it. Congratulations, by the way!

[Jon_Dahl]

As every Greyhawkian knows, Boccob's prayer goes like this:

Boccob, Bless Academicianship Knowledge Everywhere.

So that's 6 letters, then 5, then 15, and the next number is 9.

Three numbers is way too short to determine a sequence; I can make up equally-plausible answers for why the next number would be e.g. 12.5 or -85. This is not something people can answer unless they know the answer beforehand, so it's less of a riddle and more of a gotcha.

Thank you. Could I see your formula, please?

[AvatarVecna]

Most any puzzle where the "problem" is presented in numbers, and the answer is "also numbers" where what you're supposed to do with the numbers isn't specified, is mildly...doomed. Especially if the players only have a single correct sequence to analyze. I guarantee you're going to get too-smart answers before you get mildly smart ones.

One obvious way to approach a door presenting you with three digits is "X is to Y as A is to B", which leads players to go "5 is 5/6 of 6, so 5/6 of 15 is 12.5". But if they shout 12.5 at the door, they get crushed. They might alternatively go to subtraction here instead, and shout 14, which is coincidentally correct, but not for the reason they thought; that is to say, they didn't realize 5 and 15 had an intentional relationship, so if you asked them what the next two numbers are, they'd probably be stumped.

One obvious way is to see if there's some simple parabola that includes 6, 5, and 15 in that order. Assuming (1,6), (2,5), and (3,15), you end up with 5.5x2-17.5x+18. This leads to players shouting "36" at the door, and getting crushed. Assuming instead (0,6), (1,5), and (2,15), you instead end up with 5.5x2-6.5x+6, shout out "36" again, and still get crushed.

One non-obvious way is to assume it works something like the Fibonacci Sequence, where numbers A and B are used in some way to form C, numbers B and C are used to form D, and so on. This person might think "6x5=30, 30 is 15x2. Thus, AxB/2=C, and thus BxC/2=D". They do some quick math, shout out "37.5" and are crushed. Another person using the same method and the same numbers might think that instead, it's "6x5=30, and 30 is 15+15", therefore AxB-15=C, and thus BxC-15=D". They do some quick math, shout out "60", and are crushed.

One non-obvious way is that you're supposed to figure out what operations are applied between these numbers (that is to say, "6 [+, -, *, /] 5 [+, -, *, /] 15 = ?"), and you start figuring out the 16 answers. You answer with -69, -14, -13.8, -4, 0.08, 2, 5.6667, 6.3333, 15, 16, 16.2, 18, 26, 45, 81, and 450...all of them incorrect.

This is just a short walk through "why this kind of puzzle doesn't work". You can't just throw random numbers at people and expect them to figure out the way you want the numbers interpreted, especially if it's supposed to be an intelligence test, but the operations involved are basic addition/subtraction/multiplication/division. If the intelligence challenge is "figuring out the right operations", then you need to give players the answer, so they can puzzle out what operations are wrong. If the intelligence challenge is "figuring out how to get the right answer", then you need to give them the operations (and, incidentally, the operations should probably requires some kind of math knowledge above a third-grade level, else it's not really a great test of intelligence in-universe). The problem there is keeping it from being too difficult for your players (who might not be Math PhDs), while also keeping it tough enough that it's a believeable test of intelligence in-universe, and that's a fine balance to strike.

The way to approach this kind of riddle without requiring your IRL players to be as good at math as their wizard is at magic, is to make the answer not a reflection of mathematical ability, but rather something else entirely - such that anybody attempting to solve it as a math equation is already doing it wrong, and the person needs to understand something more inherent to the numbers themselves. This can involve the number of letters in the number's written form (a puzzle I've used now and then to great effect), as well as the shape of the numbers (typically, whether they have any curved lines or not, although that's usually used in relation to the alphabet). However, neither of these work as a test of intelligence to newcomers because the way to the answer is unintuitive; rather, it serves as a password system effectively, where only those with permission to be inside have been told the secret trick to getting in. Puzzles that can be solved by a clever stranger aren't very good door locks.

[Jon_Dahl]

AvatarVecna, thank you for the feedback, but the sequence is longer now. This should help.

[AvatarVecna]

Yes, somebody staring at this sequence of numbers will probably guess that "6 to 5" is "-1" and "15 to 14" is "-1", and from there they probably try out "24" or "42" (since "5 to 15" could be "+10" or "x3").

The sequence being slightly longer just changes how convoluted the incorrect answers can get. It doesn't change that there are infinitely many wrong answers, and infinitely-many wrong ways to try and solve this problem so long as you are making them guess at both "how to solve this problem" and "what the final solution is". Most of what I said is still relevant - you could still get a handful of convoluted Fibonacci-Sequence-style approaches to solving this that are almost assuredly all wrong, you can still try and solve for a base equation such that (1,6), (2,5), (3,15), and (4,14) are all points in the curve, but now instead of being parabolic it's going to be wildly more complicated. And most of those attempts are only going to happen because they're trying out maths that are more complicated than the simple subtraction/multiplication that the church of boccob is apparently using as a lock on their door to weed out the unintelligent.

And that's the part of my post you breezed past that's pretty relevant no matter how you change the sequence: any kind of puzzle along these lines is either going to be too hard for your players to solve, or too easy to believe the church is using it as a test of intellect.

[Jon_Dahl]

Yes, somebody staring at this sequence of numbers will probably guess that "6 to 5" is "-1" and "15 to 14" is "-1", and from there they probably try out "24" or "42" (since "5 to 15" could be "+10" or "x3").

The sequence being slightly longer just changes how convoluted the incorrect answers can get. It doesn't change that there are infinitely many wrong answers, and infinitely-many wrong ways to try and solve this problem so long as you are making them guess at both "how to solve this problem" and "what the final solution is". Most of what I said is still relevant - you could still get a handful of convoluted Fibonacci-Sequence-style approaches to solving this that are almost assuredly all wrong, you can still try and solve for a base equation such that (1,6), (2,5), (3,15), and (4,14) are all points in the curve, but now instead of being parabolic it's going to be wildly more complicated. And most of those attempts are only going to happen because they're trying out maths that are more complicated than the simple subtraction/multiplication that the church of boccob is apparently using as a lock on their door to weed out the unintelligent.

And that's the part of my post you breezed past that's pretty relevant no matter how you change the sequence: any kind of puzzle along these lines is either going to be too hard for your players to solve, or too easy to believe the church is using it as a test of intellect.

I promise that I didn't breeze past your points. I just didn't know how to react to them. I promise that I'm telling the truth.

[DeTess]

Basically, if you want to use a riddle, any riddle, in a DnD game, then you need to accept any reasonable answer. For example, any and all of the answers just provided by AvatarVecna should result in the door opening for the PC's. This doesn't just go for number puzzles either, but for any riddle you might use.

The reasons for needing to accept multiple answers is that if you don't, the puzzle changes from 'figuring out the answer' to 'figuring out how the DM wants it to be solved'. IE: it stops being an IC problem and turns into an OOC problem.

[Jon_Dahl]

Basically, if you want to use a riddle, any riddle, in a DnD game, then you need to accept any reasonable answer. For example, any and all of the answers just provided by AvatarVecna should result in the door opening for the PC's. This doesn't just go for number puzzles either, but for any riddle you might use.

The reasons for needing to accept multiple answers is that if you don't, the puzzle changes from 'figuring out the answer' to 'figuring out how the DM wants it to be solved'. IE: it stops being an IC problem and turns into an OOC problem.

I promise that I will accept any calculation that makes sense. I will just need to see the formula.

[DeTess]

I promise that I will accept any calculation that makes sense. I will just need to see the formula.

Then you should forget about this puzzle having a 'right' answer though. But if you run it like that, it'll probably be fine if your players are fine with basic maths.

[AvatarVecna]

I promise that I will accept any calculation that makes sense. I will just need to see the formula.

If this is the approach you're taking with the puzzle, then it can actually become a lot simpler: the temple doesn't want you to find the answer, it wants you to find an answer. As long as it's not a total guess, it'd probably be sufficient to be let in. Doing it this way, you could also have the "sequence" generated by a random number of random numbers. If whatever answer is acceptable to you as DM, then you don't need to prep it for having a particular answer ahead of time. This also makes it look more complex to people who don't know the trick.

A door lock where the solution is "creatively-applying math until you get an answer that sounds good" is an interesting approach to "clever number puzzles".

[Crake]

If you want the sequence to be solvable, it needs to repeat at least twice.

6 -> 5 is minus 1
5 -> 15 is times three (your solution), but it could also be +10 (my initial guess), or it could even be "multiply by 1/2 of the previous number", or "add a 1 to the front end of the number"
15 -> 14 is minus 1, so the first part is repeated

Note that the second step is not repeated, and thus, I could equally assume that the next step would be +10, and thus 24 into 23, then 33 into 32, or any other number of sequences.

If you extended the sequence to 6, 5, 15, 14, 42, 41, ?? then it would be plausible that they could determine the exact formula, but with what you have, the steps have not been thoroughly repeated.

[HeraldOfExius]

Given the pattern you have chosen, I would suggest that you provide at least 5 numbers in the sequence.

You have two patterns in the sequence. For one of those, you have two examples: 6 to 5 and 15 to 14. For the other, you only have one: 5 to 15. Deriving a pattern from only one occurrence can be rather difficult, since there are several ways to go from 5 to 15 (add 10, multiply by 3, add a 1 to the start, etc.) and that is the only example given of the "multiply by 3" step. Without an additional occurrence of this step, the players would literally have to guess which method of getting 15 from 5 was the intended one.

[Crake]

Given the pattern you have chosen, I would suggest that you provide at least 5 numbers in the sequence.

You have two patterns in the sequence. For one of those, you have two examples: 6 to 5 and 15 to 14. For the other, you only have one: 5 to 15. Deriving a pattern from only one occurrence can be rather difficult, since there are several ways to go from 5 to 15 (add 10, multiply by 3, add a 1 to the start, etc.) and that is the only example given of the "multiply by 3" step. Without an additional occurrence of this step, the players would literally have to guess which method of getting 15 from 5 was the intended one.

That is actually the minimum amount of numbers you would need, but I went with 6, because I think determining the relationship between 5 and 15, and 14 and 42 is more interesting (x3) than determining the relationship between 6 and 5, and 15 and 14 (-1), so the solution would be more satisfying to come to. Worth noting that most education does where I grew up did the times tables up to 12, so 14x3=42 wouldn't be an immediate connection and would take a moment.

[HeraldOfExius]

That is actually the minimum amount of numbers you would need, but I went with 6, because I think determining the relationship between 5 and 15, and 14 and 42 is more interesting (x3) than determining the relationship between 6 and 5, and 15 and 14 (-1), so the solution would be more satisfying to come to. Worth noting that most education does where I grew up did the times tables up to 12, so 14x3=42 wouldn't be an immediate connection and would take a moment.

Yeah, I was just going for the minimum. An alternative would be to swap the patterns, and get something like "6, 18, 17, 51, 50, x" so that the next step is the x3 instead of -1.

[Crake]

Yeah, I was just going for the minimum. An alternative would be to swap the patterns, and get something like "6, 18, 17, 51, 50, x" so that the next step is the x3 instead of -1.

Yeah, that's also a good fix

[Berenger]

The correct answer to that riddle is to avoid the main corridor, go through the kitchen, blow up the lateral meditation chamber wall with explosive charges and storm through the smoking crater to slaughter those disgusting, sadistic little nerdholes before they know what hit them.

[Jon_Dahl]

After reading HeraldOfExius and Crake's posts, I have decided to extend the sequence to five. Thank you.

[Biggus]

Yeah, the sequence needs to be at least one longer, as it is there are multiple "right" answers. For example, I assumed the formula was "subtract 1, add 9" which as written is just as logical as your answer.

Funnily enough, I came across this problem myself the other week, I was doing number sequences with some kids and they kept coming up with different answers which I realised fit the given pattern equally as well as mine.

[Jon_Dahl]

Given the pattern you have chosen, I would suggest that you provide at least 5 numbers in the sequence.

You have two patterns in the sequence. For one of those, you have two examples: 6 to 5 and 15 to 14. For the other, you only have one: 5 to 15. Deriving a pattern from only one occurrence can be rather difficult, since there are several ways to go from 5 to 15 (add 10, multiply by 3, add a 1 to the start, etc.) and that is the only example given of the "multiply by 3" step. Without an additional occurrence of this step, the players would literally have to guess which method of getting 15 from 5 was the intended one.

But it's okay if it's rather difficult, right?

[Crake]

But it's okay if it's rather difficult, right?

The issue is that the difficulty isn't in working it out, it's that it comes from sheer guesswork, which isn't how you want a puzzle to be solved, by just trying to guess at the myriad of potential formulas for the sequence.

[Calthropstu]

I was able to get the answer from what was presented before checking the spoiler. It wasn't difficult in the slightest.
The problem with this is: the answer, no matter how difficult, can be easily achieved by someone with an int of 3. Gather information is a thing.nothing is stopping those who know the answer from telling someone who does not. Nothing is stopping an int 5 creature from going in, hearing someone shout the answer ahead of them, going up to the spot and doing "monkey see, monkey do."

[Jon_Dahl]

It wasn't difficult in the slightest.


This is not what I want, so I feel disappointed. I will think of a new mathematical problem and come back.

[Jon_Dahl]

I have updated the OP. Let's try again.

[DeTess]

This is not what I want, so I feel disappointed. I will think of a new mathematical problem and come back.

Maybe you should consider what it is you want this puzzle to achieve IC. It seems that it is a test of someone's capacity of reasoning, so just have it be a random 3-4 number sequence (that changes daily, or even per person approaching the chamber) where the PC's have to provide the next number. This moves the focus on their reasoning, rather than the existence of a 'true' answer.

I'd also remove the ridiculous punishment. This protection is just for his meditation chambers which are supposed to be publicly available according to you, so brutally murdering everyone that makes a mistake is overkill. Just have it be a door that only opens for those the gives a good answer, and refuses to open for X days for someone that gives a wrong answer.

[kinem]

18. In this two-phase sequence, you first subtract one-third and then multiply the result by three.

9 x 3 = 27 not 28

[crayzz]

I have updated the OP. Let's try again.

Am I confused or should that final value listed be 27, not 28?

If it's supposed to be 27, then there's a slight problem in that 23 looks as valid a solution as 18. You have "subtract a third, multiply by 3" but for the values given the pattern "subtract n+1, multiply by 3" works just as well.

6-> subtract 2 -> 4->12
12 -> subtract 3 -> 9 -> 27
27 -> subtract 4 -> 23 -> 69

[Mr Adventurer]

I'd also remove the ridiculous punishment. This protection is just for his meditation chambers which are supposed to be publicly available according to you, so brutally murdering everyone that makes a mistake is overkill. Just have it be a door that only opens for those the gives a good answer, and refuses to open for X days for someone that gives a wrong answer.

Good point - if the temple says something is publicly available, but then kills a (apparently random from exterior observation) number of people who try to use it, the temple could reasonably be tried for murder under local laws and in any case might be able to expect to be burned down by the citizenry.

[GrayDeath]

9 x 3 = 27 not 28

And a third of 12 is 4, not 3.

[Jon_Dahl]

I don't know what happened with my brain. This is not my best day. I have fixed the OP.

[tstewt1921]

6, 4, 12, 8, 24... 16,

It's another way of looking at it, 6 x 2 = 12, 4 x 2 = 8, 12 x 2 = 24, 8 x 2 = 16.

[Kris Moonhand]

6, 4, 12, 8, 24... 16,

It's another way of looking at it, 6 x 2 = 12, 4 x 2 = 8, 12 x 2 = 24, 8 x 2 = 16.

Yeah, that's how I did it. When I checked the spoiler and saw them talking about subtracting 1/3 and then multiplying by 3, I was like... wat. It does work, but that is definitely not how I got the answer.

[Crake]

Yeah, that's how I did it. When I checked the spoiler and saw them talking about subtracting 1/3 and then multiplying by 3, I was like... wat. It does work, but that is definitely not how I got the answer.

I mean, it's technically the same thing, because multiplying by 3, then taking subtracting a third is functionally the same as multiplying by 2, so every number will be twice the number two steps behind it in the sequence

[denthor]

6-(2)= 4×3=12-(4)= 8×3=24-(6)= 18×3 = 54

The numbers inside are the pattern I saw. 2,4,6 multiply by 3.


I did not see subtract 1/3 to get the next number.

[Elkad]

I just read it as 2 sequences intermixed, doubling.

6>12>24
and
4>8>x
x=16

[PoeticallyPsyco]

Seems intuitive enough, but I'd recommend writing it down for the players. I think it would be a lot harder to spot the pattern just hearing it.

[pabelfly]

I'm of the opinion that the riddle is far too simple. I'd look up some riddles that you could use instead of a simple number sequence, and I'd consider using three riddles for the players to try to decipher. Alternatively, you could find a difficult puzzle game for the players to try to work out instead.

[Cruiser1]

"6, 4, 12, 8, 24... what comes next?"
Anyone who enters the corridor without shouting the right answer will face a golem...
My somewhat lateral thinking way of getting past this is to realize that technically you only need to shout the right answer at some point, and aren't penalized for wrong answers. Therefore just shout each number from 0 to 50 in sequence. The right answer is assuredly one of the numbers within that range, so afterward you're guaranteed to not get attacked.

In other words, I don't care about the right answer, and just want to get past the corridor, and I think Boccob the Uncaring would approve of my methods. :smallwink:

[Nightcanon]

Hmmm. Real-world analogies: if I want to access the 'meditation space' at my local church, I can probably just walk in provided it is open; if I want to do the same at a cathedral I may be treated as a tourist and invited to pay an entry fee. In other places or traditions, I may have to provide evidence of my bona fides, and observe unfamiliar dress customs or similar. If I want to get into the reading room of my local public library I can probably just walk in, though I may have to register first; if it's a special collection or part of a private institution, I'm probably going to have to register and/or pay, and possibly demonstrate some form of qualification or affiliation (I'm a consultant at a teaching hospital, so have access to the local medical school library, I'm a member of various professional associations so have access to their journals etc).
None of these require me to solve puzzles or answer a test to enter. I can see why Boccob might have some sort of intelligence or lore requirement, but as a game mechanic, why can't this be represented as 'must have Int >= 10' or 'must have x ranks in knowledge: arcana' or 'must be able to cast arcane spells of level y or above'.
I seem to recall from previous threads that you are a fan of riddles (and I guess, since you remain a fan, your players are okay with this). I agree with the comment that this isn't so much a riddle as a password that is effectively written down somewhere. As a puzzle it's sort of weak. Does it change each time? Is it supposed to change each time, but you've decided that the puzzle of the day will be this one when the PCs want to access the room?
Previous puzzle/riddle threads have cautioned against making 'solving' a riddle or puzzle the only way past a specific obstacle- in this instance, access to the meditation chamber might be by permission of a particular individual. How do you persuade him? Well, he's always on the lookout for donations; there's a little job he'd like doing first; you can do him a favour by helping with clue downwards 17 in today's "words in a cross" puzzle in the Daily Prophet. That way the PCs can influence the NPC in a variety of ways, including interacting with a puzzle if they wish to, without having to pull "I have a natural Int score of 19, plus age-related bonuses, and I'm wearing my Hat that says Wizzard +6. Of course I know the next number in the sequence, and I can tell you the formula for calculating the nth number in the sequence".
It's worth noting that approximately 100% (to 2sf) of people who know that a man goes of two legs in the evening because they've heard the story of Oedipus and the Sphinx, not because they have worked it out. Also worth recalling that the other contender for 'most famous riddle in fantasy literature' isn't a riddle at all, but a version of "what is the answer I am thinking of?"

[Calthropstu]

If you are looking for puzzles...

https://www.amazon.com/dp/B0725X7TGZ?tag=duckduckgo-exp-b-20&linkCode=osi&th=1&psc=1

[Randomocity132]

In this two-phase sequence

I would make sure the magic mouth specifies it's a two-phase sequence.

I was rather stuck on this for a while because I assumed the rule was the same between each number.

[Mehangel]

I just read it as 2 sequences intermixed, doubling.

6>12>24
and
4>8>x
x=16

This is how I solved it. I mean, I could've written out an equation, but I did not see a reason to.