In talking about puzzles, I haven’t mentioned maths puzzles yet. Which is a shame, so I’m rectifying that now. Why are maths puzzles good? Two reasons: one relating to the players, one relating to the campaign.

RPGs like Dungeons & Dragons may be enjoying their moment in the sun, but they aren’t quite mainstream. They are geeky activities that are mostly enjoyed by geeky people. Each group is different but I’d wager that most groups have someone with experience in mathematics.

That’s relating to your players – I’m making the bold assertion that people who like one geeky thing have good odds of liking another. Now for the in-game justification.

Riddles aren’t like passwords. Usually they can be solved by anyone. Some are harder than others but the word that opens the magic door can be deduced from clues. Why wouldn’t the mad wizard use a random sequence of letters and numbers? Or, if they want the word to be easy to remember (because wizards have poor memories??) why do they have a plaque saying that it’s those things that have four legs in the morning, two at noon and three in the evening?

(Answer: a mutant hydra that regrows legs instead of heads that gets two legs cut off and one of them is cauterised. Obviously).

The hand-waving I do for this question is that, well, that’s simply the way magic works. For whatever reason, a spell that securely locks a door works best when it is guessable. I’ve also included some wizard lairs that were tests – if and only if you were smart and strong enough to get through the puzzles and monsters were you worthy of an audience. But some riddles are meant to exclude intruders, even the worthy ones. So I bake it into the rules of magic as a weird quirk. If you have a different explanation for why wizards make their passwords solvable, I’d love to hear it.

Which brings me back to mathematics. Language is universal. Specific languages differ, but any mortal can speak any mortal language. Many settings have Common but you can’t assume intruders won’t speak Elvish or whatever. Mathematics, though – beyond basic arithmetic, mathematics is the domain of civilised races. Kobolds that trade with Dwarves might speak and read their language but, as simple tribal folk, they won’t get much practice applying mathematical skills to problems.

**Players of my Trutea campaign, skip the following paragraph. It contains minor spoilers.**

In a current game, an NPC found himself trapped in a mine filled with enemies. These enemies included kobolds and beings incapable of speech. To protect himself, he locked himself in a room and sealed the door with riddle-magic. But what riddle? Most kobolds are uneducated but they aren’t stupid. In any given clan, there’s probably a few who can read all the popular languages. But how many know any mathematics?

In this case, the maths-based riddle serves as a filter. If you can crack it, you probably aren’t a kobold. In which case, great, come on in. Any civilised person is more likely to be rescue than a typical low-level monster NPC.

This is the benefit of maths-based puzzles – they exclude savages and all civilised folk. The difficulty of the puzzle can adjust depending on your definition of ‘savages’.

Here are some maths puzzles I have shamelessly stolen. Google is great for these – better than other types of puzzles in my experience. These are easily solvable with high school maths. Feel free to adjust/substitute depending on the proportion of engineers/programmers in your group.

**Simultaneous Equations**

Straight up, unashamed mathematics. The PCs enter a room to find jars labelled zero through six. On the wall is etched:

2x+y=5

x-y=1

The PCs have to move/destroy/look inside jars 1 and 2.

**What’s next in the sequence?**

1 11 21 1211

The sequence is generated by counting the quantities of numbers in the previous entry. In other words, the first entry has one 1, so the next is 11. Since that has two 1s, the next is 21. So the answer is 111221 (one 1, one 2, two 1s). An alternative question would be: __what is the first entry in this sequence with a 3? __The answer is the next entry: 312211.

**Interesting Factorising**

Yeah, it can be a thing. For example (again, Trutea players, look away):

__What are two numbers that multiply to give 10,000 where neither has a zero?__

A bit of thought shows that 10,000 = 10^4 = (2×5)^4 = 2^4 x 5^4. Neither 2^4 (16) nor 5^4 (625) have zero, so there’s the answer. Will your players get that? Maybe. Will a kobold or goblin? Unlikely.

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You can leave these questions as you find them or give them a more fantasy feel. But really, mathematics exists in your world. I’m sure wizards use it for their spells (though that depends on the setting and your DM). Rogues might know enough probability for gambling. Other characters might find other uses for it.

One final question to get your juices flowing. I’m assuming that townsfolk know some maths but kobolds don’t. Both halves of that assumption could be wrong. But here’s a question: do angels and demons know maths? Are they powerful and knowledgeable, or is mathematics a mortal concern and thus beneath them? Maybe they are genius mathematicians; maybe they struggle beyond basic arithmetic. Who knows? But the answer could be relevant to your campaign.