# How to create a Number Puzzle? [closed]

I wanted to create a puzzle for my adventure. I found a very interesting book that has all sort of tips on how to create them: It´s called fourthcore alphabet. The puzzles there are very generically described, but it helps to give a initial idea.

One puzzle called my atention:

The crusaders enter a catacomb containing 666 numbered and decorated sarcophagi. The skeletal caretaker will not reveal which coffin is the puzzle’s solution. However, the crypt thing will truthfully answer three and only three ‘yes or no’ questions (ex. ‘Is the correct coffin marked with an even number?’). Opening an incorrect coffin harms the crusaders (Fourthcore Alphabet, page 40).

I would like to use this puzzle in my adventure, how ever I´m not sure how to implement it exactly. I would like to use doors instead of sarcophagi. I plan on trapping the players in a room with many numbered doors, where only one door is the exit.

Here are my questions, though:

1. How many doors should I use?
2. Which number should the puzzle`s solution be?
3. Which other clues could the doors have?
4. Any other ideas on how to improve this puzzle?
5. What to do if the players fail to get the right answer?

I think 666 doors are too much, I though about having 50 doors and having the answer in the door number 2, for it is the only even prime number. So they would be able to get the right answer with two simple questions (Is it a even number? Is it a prime number?).

My main concerns are: 1) making a puzzle too difficult to be solved; 2) having the players trapped in a room with lots of doors and having to use a Deus Ex to free them.

• This will happen in a temple shaped like a dragon.
• A very import hero of the world has recently been killed while fighting a Demon, inside this temple the Players will find his remainings and possible resuscitate him.
• There is a demoniac theme to this story and also a Dragon theme.
• There could also be some oneiric elements to this story, so it must not necessarily be realistic.
• We are playing a D&D 4th edition campaign, although I thing this puzzle idea is pretty generic and can be applied to any system. Specific game play mechanics ideas would be very welcome!
• Three questions is a bit of a harsh restriction, and unless the number has some specific property that the players know in advance, there isn't a good way to determine what number it is. Three binary (yes/no) bits of data is only enough to accurately determine 8 doors. If there are 666, the players have a 4/333 (1.2%) chance of success. – user8248 Jun 20 '14 at 6:28
• While a great idea, try not to have the penalties too severe, or allow the players opportunities to ask additional questions. Think like your players will-- If they try to approach it in a binary search method, they'll end up wasting their attempts. Prime numbers don't really stand out as being special to anyone who doesn't interact with numbers or math on a regular basis, so you might need to devise a way to drop subtle hints to your players if they're not math-savvy. – LeesusFreak Jun 20 '14 at 6:31
• @user Perhaps your question is a bit too broad for us to answer well... we have some text for this purpose, that starts with "There are [either] too many possible good answers..." - Perhaps you can refine your question's scope? – user8248 Jun 20 '14 at 6:41
• Tangential puzzle idea, since you mentioned doors: you could toss in the Monty Hall problem. But yeah, the format of stack exchange really doesn't mesh with this kind of thing, ya might have more luck on reddit. – LeesusFreak Jun 20 '14 at 6:45
• Hey y'all, comments aren't for discussion or answering the question. – doppelgreener Jun 20 '14 at 6:55

Ok - I'm trying an Answer...

### Purely Mathematical solution

As mentioned in the Comments the Riddle has a very low success ratio, with yes/no questions the only surefire way would be to reduce the remaining possible doors by half - maybe you can reduce them by 2/3, if you ask really cool trick questions, which are yes for 1/3 of the numbers, no for 1/3 and maybe/cannot be answered for the last 1/3. This would in the best case reduce the number of questions by 2³=8 or 3³=27 - so they could only narrow it down to 84 / 25 Doors

With 25 Doors and the Player trying random doors, they would be expected to succeed at about their 13th try. So one possibility would be, that the Party needs about 1hour to deal with a wrong door and impose a time-limit of X hours for them to succeed (for example 20 hours). They would have a small failing rate, if they choose the right door as one of their last choices. Another possibility with traps: if the Party splits up, lets say they're 5 members. So they would choose 5 out of 25 doors. This would be a 1 in 5 chance that one player chooses the right door. So they would need at most 5 tries per player.

### A more P&P oriented solution

So... are they in a temple of the great Mathematics Goddess Complexita? No? Then why the hell should there be a complex number-puzzle? Make a thematic puzzle! Make information which the player collected about the world, the temple, maybe other people trying before, local legends and so on count! Another big hint for the riddle for the players can be this ("If you choose the right questions you are guaranteed to succeed without any chance involved") So the players know there is a way to find one door with 3 Questions. They can logically deduct from there. If there are for example 100 red 100 green and 466 blue doors, they could not solve the ridde if it was a blue door, so the correct door must be red or green - but this is again very contrived logic. It would be better to narrow it down by giving the temple god/daemon a thing for certain numbers - if the god presents duality he only likes numbers which are powers of two, maybe he is a trickster and only favors numbers like 111,222,333... if the players can get this knowledge, they can reduce the number of possible doors and can ask thematic questions - like "Would the Temple-deity like digits printed on the door"...

• To be fair, the puzzle is from a fourthcore book, it's supposed to be hard/deadly. – wax eagle Jun 20 '14 at 9:59
• @waxeagle To be extra fair, the OP just stumbled over a fourthcore book that looked neat, and isn't running a fourthcore game. – SevenSidedDie Jun 20 '14 at 15:38