Messing With Players Via Math

TL/DR: Use Base 6 Math in clues

what if they dont get it
Lots of ways you might be able to sneak a math lesson into the campaign.
The DM could have an Elvish merchant appear before them selling stuff with prices shown in base 6 (of gemstones or something). The difference in expected values might clue them in on another way of thinking about numbers.
What I would do is have two quests, one that is at the actual desired location if they figure out the numbers are in base six with the things they expect to be there and more, but also one at the location if they read it in base ten with either a trap or an ambush or some other slightly punishing but not really encounter that may lead to roleplay and will lead to more clues.
They didn't figure it out by the numbers, maybe there will be another set of directions that has geographical landmarks instead of numbers (although the terrain has changed a lot, so there's still a challenge in figuring out the now vs then of the directions). Or maybe there will be someone who knows where it is there, so they need him as a guide and have to roleplay their way through that relationship.
There are other possibilities, but the idea is that even if the players screw up, unless it's a game where small mistakes or unsolved puzzles are known and expected (by the players because they like the challenge) to be punishing, their mistake can be fixed by adding new clues or going on a side-quest or something. That's part of the improvisation and the understanding that you're playing with people who think differently than you.
Then they fuckin' dddiiiiiiiiieeee!
Then they fail the adventure, same as if they don't "figure out" a combat?
Edit to add: The advice that follows from this comment is that, if you're going to have a puzzle, have a failure state that isn't just "The party sits around forever going 'uhhhh... hmmm... duuurrrr...'"
I can see my players sitting there frustrated with this. Then I would just end up telling them. Then what was the point.
I really do appreciate the effort and the share, but puzzles are just, in my opinion, super silly in dnd.
In general, puzzles which rely on player ingenuity or background knowledge can be problematic. First, it makes players who have real life high int or education get extra attention. Second, it can break the feeling of immersion. What happens if the barbarian with int 8 is played by a player who figures the puzzle out? Third, in general, people always overestimate the ease of their own puzzles.
It may also help to remember the
Holy eureka, this article is precisely what I like to find regarding DMing! This is really good stuff! Saved!
It's always horrifying to watch what you were worried was such a simple puzzle that they would figure it out instantly, derail an entire night's game and stump everyone
I just let them share knowledge ooc for puzzles I make for the players.
On the flip side, it's not very fun to have a high INT character but the DM expects you to rely on your own player knowledge to solve puzzles.
Really depends how this is used. Super interesting idea for a puzzle. If the, say, hi INT wizard can use an intelligence check, or the Elf can do a history check to get clues as to how the puzzle works, this premise in no way need test the players themselves and will still add cool lore to their world. I like it!
I agree with your statement completely. From my (albeit limited) experience I have found the contrary to be the case however.
The reason for this I believe is that I have always planned PC puts to gain hints up to and including the answer. The way this was managed (as in some cases it was time sensitive) I used time passing as an in game “cost” which was determined by players making rolls for history/ religion mainly, but also other checks where relevant (e.g.: I had a rogue that made an acrobatics check to get a better look at a mechanism that was traditionally out of reach. I deemed it possible for them to do but the rolls determined how difficult the ascent was and how long that took as a consequence). I would continue giving information, making sure to include the party as a whole up to and including handing the answer to them. There is no shame in that if their PCs would have been able to easily work it out in game. Obviously if one of the players have a eureka moment I let them roll with it. If it’s a viable solution I let them have it, after all I want to reward good logic. Not punish them for not getting my answer exactly.
I have also found where the traditional low INT barbarian getting the answer as the player first does lead to some fun moments. In the context of OP imagine if the barbarian understood it because his/her clan could only count to 5 so used base 6 for their currency system because of that? Maybe that’s just me but that would be a funny moment that recognises that the barbarian isn’t just a sack of meat on the table but a living being that still had a basic society they were brought up in and an understanding of the world.
The trick I have found is to try and keep as much of the puzzle as possible available for the PC to unpick and don’t be afraid to literally give the answer because of good PC role-play, that eleven wizard would likely know of crazy things like this you know!! Of course mileage will vary depending on the table and how you like to run your games.
Tl;dr: puzzles are finicky and can be a problem: yes Should they be discounted as a valuable DM tool: No My 2CP: don’t be afraid to give the answer and reward good PC logic and role-play over punishing them if they don’t get it. If someone does get it and it’s not a high INT character, roll with it and have fun!!
The interesting thing I like about puzzles and I will paraphrase Matt Colville is that you actually challenge the player not the character. Fighting, skill challenges etc challenge the players character sheet. So it's good to have a combination of the two. Also great article on the rule of 3, I definitely fall into the wrong on not giving enough info/options to reach the correct conclusion. Thanks for that.
Criticisms of puzzles as being problematic for relying on players to solve them are themselves much more problematic for eliminating an entire style of gameplay that many tables enjoy.
I dunno. We played white plume mountain and had a blast. It had less immersion during puzzles parts, but players loved it.
Remember there's a fine line between your players being intrigued and engaged and your players just being bored and confused.
Also that amulet is sure to end in "we got a couple, let's just brute force test every combination of what's left!"
I would die long before I figured this out.
I have a large collection of mathematical failures behind me. I'm pretty sure I would either sit back and hope one of the more scientifically minded players could solve something like this, or maybe just get sad at my inadequacies.
With LOTS of hints and guideposts “wait, isn’t this where we’re supposed to turn?” This could be great fun.
Or gamebreaking lack of fun if they don’t get the clues.
The elves only have 2 fingers and a thumb on each hand.
They come across a picture of seven trees and writing that lists them as 11.
There are a couple ways you need to lead into this. The beings either need 6 fingers or something that gives them a reason for the different base. Also they should be using different numeric symbols so its different anyways and there should be some other strong clues as to the different base like room numbers counting oddly or page numbers or other mundane items. If you have a sign in common that has miles as a unit and base 6 Arabic numbers you're just being mean as a DM.
Yes, I'd come very close to reaching this decision and you've decided me. Ancient elves had 6 fingers on each hand. There will be visual representations of said elves engraved in certain places as hints. A "Rosetta" stone artifact would also be a helpful clue and possibly an interesting encounter.
I agree throwing a sign with Arabic numbers and imperial measurements would be too confusing. I like your other clues, and believe that you should let the players fail "softly" with miscounting pages or rooms before they have a chance to fail "hard" without recourse.
While this could help drive the point home, I don't think it's necessarily true. Other cultures across the globe use different base systems, without having different numbers of fingers. The majority of the world uses base 60 and base 12 on a regular basis, for example, with no bodily equivalence. See
Personally, I like the idea of wrapping it in something non-physical to play up the cultural differences over just the anatomical.
We use base 10 because we have 10 fingers. Other cultures have used base 8 because they counted the spaces between fingers. It would do well to put in a clue that uses this, like, counting between the fingers without the thumb or try to find a tree or plant that forms in 6's. Maybe where these elves lived there were hexagon mineral formations and they were sacred to them. Describe these indicators in the elf's artifacts and artwork.
Folks, I totally understand your wariness AND your warnings--I take them to heart. I'm building in rather a lot of repetitious visual clues (repeating the 6 motif in many ways). I'm preparing hints and clues for when the PCs take History and Intelligence checks. I have an NPC in mind (mini-quest to find this person likely) who will also provide further clues. I see in retrospect I worded my original post too maliciously and malevolently. I have been DMing since the advent of AD&D and I assure you: I do know better than to simply dump a complex, college-level math problem on my PCs without any recourse or in-game nudges.
Thanks for the reminders!
Why have it be elves? There’s a perfectly awesome race of creatures far more ancient and alien than elves... spellweavers. They have 6 arms, and can regenerate 6 times. 6 is an especially sacred number to them.
Well I think the warnings have been covered so I just wanna say I think its a pretty fun puzzle, definitely envious of your players 😂 have fun!
There is a lot of negativity in the comments but I pepper my games with puzzles like this. The key is to ensure that the puzzle won’t stop the players if they don’t get it. Make the puzzle be 100% upside for solving. In my experience, 9/10 they overlook it, but when they do find one they feel like geniuses.
I love good riddles, but without trying to spoil your fun, but unless you have really math invested players like engineers, it or math graduates or students, they will definitely be completely blind and never solve this.
I have a grou of exactly those kind of people, two physicists, two IT and one bio-chem engineer and anything like this would be unsolvable by them.
But a binary, hexa, octa or chemically based riddles will be solved in minutes.
You just have to find a middle ground and unless you give them a lot of hints and they know about other counting styles like binary, hexa or octa, they will definitely be stumped and get frustrated.
If you can provide a number of hints that don't take away from the problem but lead them in the right direction this could be great especially if the party likes math and critical thinking. The problem with math related riddles is that if people don't like it they're less likely to think in creative ways because they just figure is a math problem.
heh. Reminds me of the time i had a long equation that i'd run across and i put it in a dungeon on a wall. On the door was a little chalkboard and a piece of chalk. The corridor right before the door had a spiked ceiling. There was also an equal sign on the door to the left of the chalkboard.
The door required one to move the chalkboard aside and pull the lever that unlatched it. The equation had nothing to do with opening the door, it was just the architect of the vault being a massive math nerd.
Sounds exactly like the kind of problem nobody would get and it'd become tedious
I find these systems make the most sense for races that have the same total number of fingers. We are base 10 with 10 fingers.
Tell that to the Babylonians. They used a base 12 counting system and I'm fairly certain they only had ten fingers.
This is a great idea (and I'm saving it for later) but make sure your players like puzzles (and math)! Nothing ruins an adventure like a puzzle no one can figure out.
I have all spectators use exclusively base 4 numbers.
Usually players don't clue into this and just assume they're crazy tho.
“To reach it, they must navigate the 6 trials”. Unless this is a translation to common written by someone who understands base 6, this is written wrong. If it is in Elvish, it should either be “six trials” or “10 trials”. If you really want to screw them up, it was written “10 trials” in Elvish and they found it written in common by someone who didn’t understand so wrote “ten trials” (don’t do this unless you know someone in the party had a reason to be thinking about other bases (pre game conversation, you know yesterday was towel day, many people don’t realize that when “what is six times nine” was written in the scrabble board that was 42 in base 13).
Yes, good point. This will likely be the first clue I leave them. A scholar knowledgeable in Ancient Elvish will point out that the amulet accommodates or corresponds to 6 (common lang.) trials but the written lore he knows says 10. He cannot fully explain that discrepancy but he suspects that 4 trials have not in fact been forgotten. Thanks!
Well, sheesh, I wouldn't leave them hanging for-fricking-ever. I have an elf and half-elf in the party, a bard, and NPCs in the pipeline. I wouldn't just leave them hanging in the wind. But I will enjoy watching them twist just a bit. And even knowing it's base-6, you have to convert correctly. There are any number of intermediate steps that I can help them reach the ultimate goal.
I mean you know your players better than any of us here do, but are there even any remote chances that at least one of them even knows that base 6 is a thing?
You could throw me all the 6's you want and I still wouldn't have a damn clue what to do with that. And even if you'd told me it's in base 6, I still wouldn't have a damn clue how it works.
Some people are giving shit, but I disagree. Yes it isn’t for all parties. My current players would get a kick out of it though, especially if there are multiple obvious clues the puzzle (Elven players can make history checks, murals of “the ten gods”, and Npcs as someone else said). Also let there be simple (f*** this let’s break down the door) solutions.
But I do think it is an incredible way to add a layer of depth to an important dungeon or culture. You don’t have to make it a whole big thing if set up correctly, and I think it’s a good idea to remind players of how culturally diverse your world is.
I have a politically heavy, serious tone, low magic game and it’s difficult finding puzzles that don’t involve the same overused riddles, boring traps, or random mechanism. Instead we have a puzzle that makes elves or whoever you choose, more alien in origin.
Note: This should only be used ONCE in any given campaign. Math sucks. Don’t force it.
I would get this as a player but only because I am good at math AND base 6 is my favorite. Like even if this was base 7 or 8 I wouldn't get it.
I use base 6 specifically for things I don't want my players to piece together, like labelling maps when I don't want my players to piece together the order of numbered rooms in a large dungeon. I'm impressed with your players if they can piece this together.
Why is it called the 6 Trials of the Karath Hen-iorech if its in Base 6, and 6 is, essentially, 10?
I feel that'll throw off anyone in your party.
Alternatively, name the challenge the 10 Trials, and when the players see there are only 6 trials it'll be an extra clue.
So what awaits them at the base 10 location?
Remember the Three Clue Rule ... I love the quote from
be sure to give them another way to figure it out, like having it so the elves have 6 fingers on their hands or something, which they can deduce/know by looking at elf skeletons along the way or having ever met an elf.
Use base 2, 12, or 16 rather that 6. Base 2 is binary, used for all computers and easy to replicate with any 2 symbols, good for not using numbers. Base 12 is actually used in some parts of India and south Asia and has quite a few advantages over decimal. Base 16, hexadecimal, is basically binary but easier for people to read.
Base 6 is like base 12, but just less useful.
Unless you're letting a knowledge history check know they used base 6, using it is just lying, any number in base 6 will look like a base 10 number. But with base 2 (with symbols other than 0 and 1), base 12, and base 16 you need to introduce new symbols. So one of your clues, after they've done others or maybe not even connected with the clues, will say "A5 miles". Now they have an actual clue that the numbers are weird.
I think this is definitely something you could only use with very specific groups of players that you knew well. They have to be good with math and enjoy puzzles. My current group is all engineers / computer scientists (myself included) so the math part would be fine but I'm the only puzzle guy in the group. If I threw this at them I think they would get bored long before they figured it out.
Also, definitely need like a million easy to find clues. Switching to an uncommon radix is a very rare puzzle trick so it wouldn't be something most people would think of. If you did this in something more common like binary (base 2), octal (base 8), or hexadecimal (base 16) I think people would be much more likely to pick up on it because they have probably seen it before.
Having studied binary, hexadecimal when doing computer programming, I can firmly say that while I might know about this stuff when I have cause to think about it, I would NEVER come to the conclusion that this is the solution to the puzzle.
Further I don't really understand the connection between having 6 trials, each revealing the one digit of a combination with the fact that the elves use a base 6 numbering system on maps and the like. I mean a brief case with in built combination locks typically have 6 digits on those wheels, doesn't mean it's a base 6 system being used.
So they can read Elvish, but won't already know that the Elves used base-6?
Seems like if they learned the Elvish for 1, 2, 3, 4, 5 in school, they would have raised their hand and asked "What's the Elvish for 7 and 8 and 9?" and been told that the Elves didn't use those numbers.
24 miles is 38.62 km
ANCIENT elves in my realm--thousands of years back, pre-cataclysm--counted Base 6. Contemporary elves have a less sophisticated, more integrated society.
What if a character is a scholar with Int 18 run by a player as dumn as a rock? The whole puzzle becomes a simple int check
Theoretically, yes, and I'm cool with that. Even a blind squirrel gets the nut every now and again. The puzzle doesn't equal the campaign. But I also have the opportunity to dole out information as I see fit: In dribs and drabs all the way up more tantalizing and revealing clues.
If you count from 0-5 on one hand and then, when you reach "six" you hold up a finger on the other hand and none on the first, that way the logic of the numbers going from 5 to "10" is simpler to understand. ✊,☝️,✌,👌,🖖,🖐,☝️✊ ,☝️☝️, and so on. At least it worked for me.
Oh man, I love this idea so much, but then again I am that player at the table everyone hates who wants to solve complex and difficult puzzles. It frustrates me when I'm DMing, because no one else I know likes to solve this kind of puzzle.
I'd say before finalizing this, make sure there are some serious clues to help them out if they do get stuck (maybe a previous adventurer who never made it past had almost cracked the code, but all that remains is their journal of wrong solutions which points them the right way) and make sure one of the nerds at your table is gonna have a good time chewing on some math stuff.
I love it as an idea, but I also caution you that it's exactly the sort of thing that has a "wrong answer" that the players can stumble into, and they may well get frustrated since that wrong answer is 24 miles away.
You need new symbols for enumeration. 1 should not be 1, but ■. 2 should be ●. Integer 6 should roll over to 1/ ■ and increment up again until reaching 2 /●. Check out Hex as an example.
Actually hex uses 0-9 as normal, A-F are used for the placeholders for values of 10 to 15.
wouldn't it be 1,2,3,4,5,6,11, not 0,1,2,3,4,5,10? when asked to count to a number you start with 1 not zero. for example a 6 figure being would start counting their first finger with 1 not zero...
No, you're forgetting that 0 is itself a digit. For comparison:
Base N uses N digits, but because 0 is itself a digit, the maximum single digit in base N is (N - 1), not N.
So 0, 1, 2, 3, 4, 5, 10 in base 6 is correct.