I hadn’t really planned to write a game for IFComp this year. My game last year took a lot out of me, and I had a major non-IF project on my plate for this year. But when the spring term ended and I had some free mental space, the core mechanic for Junior Arithmancer popped into my head, and I ran with it.
I can’t pinpoint (or maybe I just can’t remember) exactly what it was that generated the idea. The in-game credits for JA mention my own game A Beauty Cold and Austere, Arthur DiBianca’s The Wand, and David Fisher’s Suveh Nux. These were part of the stew of things bubbling in my head at the time, but they’re not all of it. (In fact, the source code for JA has a comment under this text that says, “FIX THIS!!,” by which I meant to remind myself to flesh out the credits. Which I didn’t do.) There’s not really a nice, linear narrative that explains how JA came to be. It’s probably more accurate to say that it’s the result of me pondering puzzle design for a lot of the past year. So that’s what I’m going to talk about.
Some Random Thoughts on Puzzle Design
I enjoy a good story, but it’s the intellectual challenge of solving puzzles that keeps me coming back to IF, as well as what interests me most as an author. Writing A Beauty Cold and Austere helped push me down this path, I suppose, as I continually had to think “Here’s a math concept. How do I present it in an engaging, interactive way where the player’s experience with that concept must be mediated through text?” The puzzles in ABCA aren’t obstacles in some narrative (at least in my mind), they’re the core of the gaming experience that I was aiming for. Or, to put it another way, in some sense the puzzles ARE the narrative of ABCA.
So, what do I like in puzzles? I like choices. I like a single mechanic used in multiple, creative ways. I like reasonable “failed” attempts at solving the puzzle to give interesting responses. I like puzzles that have some kind of underlying logic that is fairly easy to understand yet feature a combinatorial explosion in the space of potential solutions. So, thinking through to a solution involves not so much trying to guess the author’s mind as it does using the logical rules that you know the system obeys - but in creative and possibly out-of-the-box ways. (In other words, I like math. Not surprising it’s my profession.)
Some games I’ve been thinking about in the past year in terms of puzzle design and why:
The board game Ticket to Ride. It’s got easy-to-understand game logic and that combinatorial explosion in the size of the solution space. Finding the best solution - even if you weren’t competing against other players - involves solving a problem that is known to be computationally intractable. (For those who know what this means, you’re solving an instance of the Steiner tree problem, which is NP-hard.)
Domestic Elementalism. You play as a witch who can transform any object into its earth, air, fire, or water form. This quadruples the number of possible ways to interact with the items in the game without tossing a huge, complicated mechanic at the player. (We all have mental associations with earth, air, fire, and water, for instance.)
The Wand. The titular wand has three sections, each of which can be set to ten different colors. This very simple mechanic has 1000 possibilities for potential spells. Admittedly, most of the combinations don’t do anything (what a nightmare to write that would be!), but the game’s still a lot of fun. On the other hand, could you attach some kind of meaning to each of the colors on the wand, so that combining them would produce effects that the player could predict if they thought through them? The Wand is already probably my favorite IF puzzle game, but that sounded like an even more fun game. (There is a little bit of that in The Wand, actually, now that I think of it.)
The Witness (Jonathan Blow’s game from 2016, not the Infocom game from the early 1980s). This game blew me away. The puzzle mechanic is just constructing routes through grids (kind of like Ticket to Ride, actually). It’s easy to visualize each grid, so it’s easy to see what kinds of solutions are allowed and how to try different strategies. Also, the game does a fantastic job of starting off simple and then throwing more and more complicated variations on the same basic idea at you. (Really, I can’t think of another game that does this so well. If you like puzzle games, you should go play The Witness. Seriously.) But The Witness is so visual. How could you create something like that in text?
My own game from last year. Those number spaces were underutilized. I should figure out how to use them in some way that makes sense. But how could you travel from one space to the next? Arithmetic operations, of course. But why would you want to do that? And how could it be made fun for the player?
Suveh Nux. Those spells in Infocom’s Enchanter series were really cool, but in Suveh Nux you can use spells as modifiers to other spells. This greatly increases the number of things the player can try.
Threediopolis. In that game, you’re recreating strings of symbols using a set of rules small enough to be manageable but large enough to be interesting. (That’s the core mechanic of JA, actually.)
Also, Mathbrush keeps telling me that most of the responses you get when you’re playing a parser game are error messages. How to write a game that doesn’t explicitly constrain the verb set while nudging the player toward a style of play that cuts down on this problem?
Somehow all of this tumbled around in my head, and with that flash of inspiration that you can’t always explain JA was born.
Writing the Game
Originally the goal was just to complete the number sequences. And then I kept thinking “What about this? And that would be interesting.” Thus the task page came to be.
I always knew I wanted something of a story in the game, even if the player is mostly a passive observer. It was pretty easy to write. Most of my adult life I’ve been a student or a professor, and so I have plenty of fodder for a caricature of higher education. (There’s a reference to Michael Coyne’s two games in there, too. Illuminismo Iniziato, which I had beta tested and loved, had just won Spring Thing and so was also on my mind.)
While running my own tests on the game I ran into a problem I hadn’t anticipated. Glulx has a maximum integer capacity of just over 2 billion, and you can combine the spells in ways that will generate numbers larger than that. This was going to ruin the player’s sense of immersion in the game! I was really frustrated and disappointed for about ten minutes, until I remembered the improv motto of “Yes, and…” O.K., let’s just make the integer overflow a feature of the game and write a puzzle where you have to contend with it. (Andrew Schultz later called this a “fun evil” puzzle during testing. I’m good with that.)
JA still felt a little too number-focused. Was there some other dimension to the number spaces I could add that would increase interest and provide additional challenges? The idea actually hit me during a run one morning - colors! The Witness uses this to great effect, after all. So then it was just a matter of mapping colors to numbers in a way that made sense with the arithmetic theme. (Some folks who have figured out the color scheme will understand precisely what I mean when I say that the mapping is actually quite fundamental, from an arithmetic standpoint.)
My very first beta tester was my ten-year-old son. After five minutes he pronounced it “boring.” (There’s nobody like your kids to be honest with you about this kind of thing.) I completely revamped the intro so that the player was thrown into the puzzle-solving more quickly, and I front-loaded positive feedback to help draw players in.
Mathbrush recommended the side window. I had thought of that but didn’t want to implement it because it sounded too hard. But I knew he was right. So I made the effort to work it in.
When I sent the game to Arthur DiBianca one of the tasks was to complete a specific number with four spells. He and Andrew Schultz kept pushing me to optimize the numbers further, and between the three of us we found two more ways to complete a number with four spells plus a way to complete a number in three spells. So the two of them definitely helped improve the challenges on the task page.
A Few Final Thoughts
All in all, I was happy with JA when I finished it. I thought I had written a game that I would enjoy, which was my goal. I wasn’t sure how many other people would, though. For instance, I know that mathematics is an automatic turn-off for some people. But I was pleasantly surprised (O.K., let’s be honest: I was shocked) at how well the IF community received my very math-heavy game A Beauty Cold and Austere last year. So maybe, I thought, there’s a sizable chunk of the community who would enjoy JA as well, which is really all I could ask for as an author. (And then JA got 7th place, just like ABCA! Wow! And 2nd place in Miss Congeniality - double wow!! It’s far better than I expected when I was writing the game.)
Of course, Junior Arithmancer isn’t really mathematics - if by “mathematics” you mean what mathematicians like me actually do. Arithmetic is to mathematics as spelling is to writing. It forms the building blocks of much of what you do, but as a mathematician or as a writer, it’s not what you actually do.
JA is probably better thought of as a collection of number puzzles. It might not even be too much of a stretch to call it a wordplay game - just one with an unusual alphabet, together with an intricate but well-known mechanism for manipulating the symbols that make up that alphabet. Threediopolis, say, but with different “letters.”
Before I end this postmortem, a confession: When I replayed Junior Arithmancer all the way through last week for the first time since the Comp started, I did not remember how to solve all the puzzles. (Is that funny, or sad, or comforting - for a player, to know the author doesn’t remember how to solve all the puzzles?) I knew that would happen, though: It happened every time I tested the game after putting it down for a while. For instance, I totally forgot how to do zeta(2) in five spells, and I had to think for a while on sqrt(3) as well. Even though I remember the logic for producing the color scheme, I still had to reason through how to solve the pale azure, gray with a hint of violet, and rainbow tasks. Also, I cannot ever remember exactly how to get a number larger than two billion. I really had to think carefully through that one. I know the structure of JA makes this kind of thing more likely, but I wonder how many times an author has forgotten how to solve some of the puzzles in their own game.
Also, I just posted Release 2 of JA on the IFDB. It adds a little more hinting at the beginning, corrects an interesting bug, and increases the number of bonus points available.
Finally, to all of you who tried Junior Arithmancer: Thanks for playing my game.