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[Clockwise]

(This is an expansion of my original topic: http://forums.tigsource.com/index.php?topic=46020.0)

I am a fan of game series like Dr. Brain and Professor Layton that are more like puzzle books compared to games like Braid, Antichamber, and Portal (although I do love these just as much.) The former tend to provide a more "modular" puzzle-solving experience--similar to doing math exercises at the end of a textbook chapter--complemented by an overworld and story of some kind. Generally, these games don't rely on player reflexes, and players are free of external pressure (such as time-restrictions or enemies.)

My aim would be to create a game that offered the same experience, but with a focus on interesting and fun math problems.

That is the broad goal. Now I'm in the process of narrowing down various dimensions of this game. I'll go through each one:

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Problem Scope:
Games like Dr. Brain and Professor Layton contain a wide range of different puzzles that require the player to use many types of problem-solving skills--verbal, visual, mathematical, etc. This game is obviously different in that it will focus solely on the mathematical. Given that math is a massive body of knowledge, a subset needs to be selected. At the moment I'm leaning towards a focus on probability.

Probability questions are easy to pose and understand, but at the same time may be excruciatingly difficult to solve--perfect for a puzzle game in my opinion! For example:

Coupons in a cereal box are numbered 1 to 5, and a set of one of each is required for a prize. With one coupon per box, how many boxes on average are required to make a complete set? (Taken from the book Fifty Challenging Problems in Probability by F. Mosteller)

There is also the possibility of increasing topic-range to include geometry. Geometry problems also tend to be fairly simple to understand, but still require a lot of thought.

Problem Difficulty:
This one is important as it, along with problem scope, determines the game's audience. I received a good suggestion that there should be an optional tutorial mode. This would work as a brief lesson for those at the appropriate level of math-knowledge, but also as a refresher for those who need it. That said, I don't want this to be a traditional educational game--it should be more to math as what Dr. Brain is to logic, if that's clear.

It might make the most sense to offer varying levels of difficulty within each problem domain, as Dr. Brain did. Additionally, a feature similar to hint coins in Professor Layton is also likely to be included.

Narrative/Characters/etc:
This is what really separates the game from being a virtual exercise sheet. I haven't decided on a story at this point, but I'm sure that its focal character must be a professor! This satisfies me, as a fan of Dr. Brain and Professor Layton, but also makes sense if the player is solving difficult math problems throughout the game.

I'd also like it to be light-hearted; I always welcome humor in games, and there is certainly no good reason to exclude it here.

Non-Puzzle Gameplay:
What is the player doing between problems? It's almost certain they'll be navigating an overworld, but how? Dr. Brain and Professor Layton have similar room-to-room navigation interfaces, and within each room everything may be clicked on to explore it. This works, but there are alternatives. Top-down, classic JRPG view is also possible. One of my favourite lesser known logic games, Professor McLogic Saves the Day, has this type of interface. (Side note: if you like logic puzzles, you MUST play this game. It is free at http://rpgmaker.net/games/456/. It is in fact the game that inspired me the most for this current project!)

Puzzle Presentation:
What will the puzzle presentation screen look like? One aspect I haven't heard explicitly praised about the Professor Layton series is the unique picture that every puzzle has. For visual puzzles, it's certainly necessary, but for others it at least provides something for the player to look forward to (perhaps not consciously).

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This is most of what I've been considering as of late. When these are settled I can begin planning the development; questions about game engines, platforms, etc will be pondered in time. My background is in programming and I'm also familiar with the popular group of commercial game engines so it will be figured out.

Anyway, I would really like to hear from anyone who has some ideas about this. I'm open to anything at this point, so don't hesitate.

[wccrawford]

I don't really have any suggestions, but I wanted to say that I love that you're making a puzzle game.  Layton/etc are some of my favorites, but even more focused puzzle games are great. 

[Rarykos]

Coupons in a cereal box are numbered 1 to 5, and a set of one of each is required for a prize. With one coupon per box, how many boxes on average are required to make a complete set?

An average person who hears this will shake his head and say a number like 100, because that feels about right. And he will not care about rules of probability and how it works, just what feels right to him. But a person who knows this stuff and knows how to solve it will go "Ok, let me get my pen and start mathing (it's a word now)".
 So you have this contrast between a person who has no idea and will never get the right answer and someone who will get the perfect answer. Because the latter understands the rules which are too complex to be explained in a game.

The biggest difficulty in making good mathematical puzzles is in presenting them as simple and quick to solve.
There's a lot of people who like solving puzzles and thinking about solutions but don't know math formulae. When presented with a puzzle they usually come up with their own heuristic algorithms or try to do it "by hand", like drawing every set of coupons until they can come up with a solution.
 That's why the best puzzles are the ones that let you come up with your own way to solve it, like sudoku. Without depending on math knowledge or anything else than common sense or logic.
 
I think that's why games don't usually do puzzles based on probability, set theory is much simpler to understand and people can solve puzzles either by thinking a lot or by trying a lot. Simple puzzles like:
"You have 3 coupons of different colours. How many different ways to arrange them in a sequence are there?"
I can think hard about it or I can use a math formula or I can draw coupons until cows come home but this puzzle is getting solved! My every attempt and action brings me closer to the correct solution. If my solution is wrong that's because I made a mistake, not because I don't understand the rules.

Probability problems are easy to understand but coming up with a solution is very difficult. People (myself included) don't know where to start, unless they know formulae or heard this problem before. I understand what you want from me, and I get the situation, but I have no idea what to do, even drawing coupons doesn't make sense. At that point I start blaming the puzzle for being too difficult or not logic-based, because it's annoying to understand the problem but not being able to solve it because you're not a mathematician.

Suggestion: Puzzling Stack Exchange - they have some great math puzzles I enjoy solving.

Puzzles really make me feel stupid and I hate that feeling of "well, I don't even know where to start, I've tried everything, shame, on to the next game!". 

[J-Snake]

Reminds me of a fun story somehow:

Long time ago a friend of mine played Baldur's Gate 2 and there was a riddle that goes as follows:

"A princess is as old as the prince will be when the princess is twice as old as the prince was
when the princess's age was half the sum of their present age."

You have now to guess how old they are.

My friend didn't want to screw it up and called me to solve it for him. I grabbed a pen and paper and after some minutes the linear equations were solved. And he was happy he could count on me.

Surely, these type of riddles would do better in another game, but it was a nice gimmick nonetheless

[Clockwise]

wccrawford: Glad to hear it! Since you have experience with the genre, I'd be interested if you ever want to chime in.

Rarykos: I completely understand where you're coming from and really appreciate you sharing your insight. You're right that these types of questions don't have the general appeal of those that can be solving by a wider range of techniques, and I'm curious if you think there's any way the game could make itself more accessible without compromising the math-focus. What do you think would help you stay with a problem longer?

As mentioned, I'm strongly considering an introductory tutorial to provide a base set of knowledge for the player to work with. However, it would most likely not be very thorough because I don't want the game to become a lecture. Even so, I'm not sure it would be enough to help players overcome that overwhelming sense of helplessness that comes when they don't know where to begin. I do think that a hint system would be beneficial here, but I'd love more ideas on that front. Another option is to give players some amount of skip credits they can use if they're 100% stumped.

J-Snake: That's the power of math--solving problems and strengthening friendships

[oahda]

Skipping, knowing you were still unable to solve the problem isn't satisfactory in the least. You just feel like a hopeless idiot.

[Clockwise]

Princessa:

That's a good point. It's always upsetting when I can't solve a certain problem, and having to press a "Give Up" button would feel like admitting complete failure.

There is the alternative option of offering a "Save For Later"-type mechanism. Especially given that these types of problems tend to require more time to ponder over than a Professor Layton puzzle, it makes sense to let the player put a problem on the back-burner. However given that the player is supposed to be advancing through some narrative, allowing the player to simply put every single puzzle on hold would feel kind of silly so there would have to be a limit of some kind.

It's inevitable that a completely stumped player will have to admit defeat. As I said, I enjoy solving puzzles, but even so, failure is always personally upsetting. This vulnerability is the risk puzzle-attempters accept when they give a complete and honest effort, and there's no real way to avoid it.

I am thinking now about ways the game can make failure feel less devastating, so less confident players don't quit immediately. It would be important to try to prevent the player from feeling worse than they likely are already--there can't be any big red X's, sad faces, etc. Words of encouragement are also a good idea. The game is intended to be particularly challenging, so it should be made clear to the player that failure does not imply they're hopeless in any way.

[Rarykos]

 I think at this point you need to decide if you're making an educational game, where you would teach people about basics of probability. Then you have to keep in mind that educational games are usually aimed at children and probability is way above them. What kind of players would like to play an educational game only about probability? You need to consider the risk that you're making a game for a non-existent audience.  

 Puzzle games don't do math problems because they are quite abstract and difficult to imagine. That's why in games like professor layton or that ukrainian sherlock holmes you have a lot of puzzles about geometry or logic or narrative. A player needs to have an image of his solution. I can imagine how shapes interact or how the context of the story impacts this puzzle. That puzzle about a princess illustrates this best- I can't imagine any solution, the puzzle is just about numbers that have nothing to do with anything in the game world. So the only way to solve it is to use your math knowledge. I have no context to help me find a solution.

 However, if it's clear from the context that the princess is about 15 and the prince is about 40 (because you can see how old they look) you have these restrictions that make you think there is a simple solution. If I want, I can try every number combination! And eventually I'm going to find the right one. I can take a piece of paper and try! Because I can imagine something tangible I have a feeling I know my solution. And of course it's quite a big hint, but still if you don't solve it using linear equations, you'll waste some time.

 So the way to make math puzzles interesting is to ground them in the narrative, to make the player care about the outcome, it's not just about numbers now. What matters most is letting the player know there is a good way (using proper math) and the hard way (trying 30 different combinations) to solve it. And the player knows that he doesn't have to check every single natural number to solve it the hard way.

But in a puzzle game all math puzzles need to be very simple, so a player can write it down using his basic knowledge and even if he doesn't know needed formulas he can try putting in his guesses. Unless you want to give lectures on everything and it becomes an educational game.

There's also a way to educate players without breaking immersion. When a player has to solve a math puzzle he has a piece of paper that already has different formulas written on it. And then every time that a math puzzle comes up, he can consult his piece of paper, find the proper formula for this problem or he could do it on his own. Maybe he could find additional formulas in the game, so now he has a formula to help him solve that puzzle that he skipped. Maybe it's not just formulas but also steps how to solve a problem using formulas!

I like the way you're designing this game! Makes me think you can actually make it a good game

[Clockwise]

Thanks for the response... and sorry for my late reply.

You bring up many valid and interesting things for me to consider!

Puzzle games don't do math problems because they are quite abstract and difficult to imagine.

I've been thinking about how to deal with this problem in the context of probability. At their core, most probability problems present experiments to the problem-solver and ask them to calculate the probability of some possible result of the experiment.

Ex: I roll three dice. What is the probability that my total roll value is 7?

Here the experiment is rolling three dice and it gives some result (D1, D2, D3) each time. Counting every dice as unique (e.g. the roll (1, 3, 3) is different from (3, 1, 3)), this experiment has 216 possible outcomes. Every outcome has some total sum, and so finding the probability of the sum being 7 is equivalent to finding all the experimental outcomes that have a total sum of 7 and dividing it by the total possible outcomes (216 here.)

That is a more analytic approach to the problem, but perhaps the game could offer tools for players to use that would allow them to avoid this. As I said, the player is trying to predict the results of an experiment, so what if the player was able to actually create the experiments and see what happens for themselves?

For the above problem, it would be easy to provide the player with some interface that lets them simulate dice rolls and count certain outcomes for them. With more complicated problems, the challenge for the player would be translating experiment descriptions into something they can create and run themselves.

I'm still not sure how I feel about this idea because it seems like it changes the entire focus from math to something quite different. What I like about it is it presents more of a ground for the player to walk on in the face of the potentially intimidating abstract nature of these problems.

So the way to make math puzzles interesting is to ground them in the narrative, to make the player care about the outcome, it's not just about numbers now.

I agree 100%! That is one of my goals with this game; I want players to be motivated to get through the problem because they care about continuing through the narrative. Ideally, they would enjoy solving the problems as well (I don't think even the best narrative could overcome an absolute hatred of puzzles), but the narrative and game-elements could provide a push that would otherwise be lacking from a textbook.

There's also a way to educate players without breaking immersion. When a player has to solve a math puzzle he has a piece of paper that already has different formulas written on it. And then every time that a math puzzle comes up, he can consult his piece of paper, find the proper formula for this problem or he could do it on his own. Maybe he could find additional formulas in the game, so now he has a formula to help him solve that puzzle that he skipped. Maybe it's not just formulas but also steps how to solve a problem using formulas!

This is a really good idea. I like the idea of players unlocking formulas as they progress. It's sort of like a very nerdy parallel to discovering new weapons or upgrading in an action game Most importantly is that it would let a player know what's expected of them. For example if they only have two formulas in their toolbox, they would know that the current problem must be solved with at least one of those. Hints could also point the player to the relevant formulas.

I like the way you're designing this game! Makes me think you can actually make it a good game 

Thanks, I appreciate that! I can't make any guarantees that this will be made; I wouldn't begin development unless I had something I really believed in. As is apparent from this discussion, I still haven't convinced myself it's worth pursuing, but I enjoy working at it, bit by bit. I have also begun thinking about another puzzle game--this one more appropriate for a general (well, at least puzzle-loving) audience.
 

[Rarykos]

I think you're absolutely right that it's very difficult to keep this focus on probability and still make an accessible game. Having an interface to get a feel for the numbers would be interesting, like those old physics simulation games, but it's too unreliable. The player could roll and roll and never roll a 7. It would make a fun toy though!

Personally,I feel like the best way is to make a choice-based game. Locking content until player solves the puzzle and gets the exact answer (like it's usually done) is just one mechanic. Probability gets interesting when it influences your judgment. Like, how probable is it to roll a 7, because then you know if it's worth gambling.

More specifically, how probable an event is , because that tells you if this person is guilty. And then you make your call, keeping in mind your probability and other clues you decide if he's guilty or not!
That's how I would do it, noir puzzle game! 

I understand your concerns, it's good you're taking your time. Good luck with the other one!

[Clockwise]

Having an interface to get a feel for the numbers would be interesting, like those old physics simulation games, but it's too unreliable. The player could roll and roll and never roll a 7.

I did consider that possibility. To go along with the experiment-building would be a way to run the experiment multiple times. The player could instantly see the results of 10,000 experiments and get a good estimate.

Personally,I feel like the best way is to make a choice-based game. Locking content until player solves the puzzle and gets the exact answer (like it's usually done) is just one mechanic. Probability gets interesting when it influences your judgment. Like, how probable is it to roll a 7, because then you know if it's worth gambling.

I think this is a really great idea. Changing the game so that the player will progress whether or not they know the correct answer could result in some unique game experience. Players who know more probability will be at an advantage, and it wouldn't prevent others from continuing if they're stumped. Players might finish the game with a bad ending and wonder how they could have done better--maybe they'll study up on some math! (Maybe not though.)

Solving mysteries is also an intriguing setting for such a game. The player could work through a series of cases and depending on which cases they solve, the story would play out differently.

[Rarykos]

Oh I understand, that's a good idea! 

Well, at least they'd notice something is wrong.