The Reasoning Behind Video Game Puzzle Design
How deduction, induction, and abduction are applied in puzzle games
If puzzle games are about making us think about something, then thinking about puzzle games is about thinking about our own thinking. In other words, “how do we reason to solve puzzles?”
To answer that question in this essay, I show how puzzles in video games can be divided into three categories of reasoning, which are well known in the areas of logic, mathematics, and philosophy:
- Deduction
- Induction
- Abduction
All types of puzzle design in video games require one or more of these forms of reasoning to solve the problems posed. This is true from those puzzle games that innovate on features of traditional table puzzles, such as Gorogoa, to those with completely unique mechanics, such as Baba is You.
How do we figure out how to advance in Limbo, how to solve the GLaDOS tests in Portal, or how to solve a murder in Return of the Obra Dinn? If you think about it, you will notice that puzzle games deal with very different ways of thinking. This is one of the factors to explain the fact that a good Limbo player will not necessarily be good at solving puzzles in the Professor Layton series or Return of the Obra Dinn and vice versa.
In fact, the three games above are good examples of puzzle games that require mainly, and respectively, deductive reasoning, inductive reasoning, and abductive reasoning. Thus, someone who is skilled with deductive reasoning, will not necessarily be an abductive reasoner, and so on; although all these forms of reasoning have elements in common.
Next, we’ll find out what these forms of reasoning are and how they apply in some examples of puzzles in games.
Deductive Puzzles (Logic Puzzles)
Deductive reasoning is logical-mathematical reasoning. That is, it’s mostly employed by logicians, philosophers, mathematicians, and computer scientists. This type of reasoning operates on formal patterns over sets of linguistic symbols or geometric shapes. However, the main peculiarity of deductive reasoning is found in the field of argumentation.
In logic, we say that an argument is deductive when, since their premises are true, it is impossible that his conclusion is false. In that sense, and assuming that an argument can only be either true or false, there is no such thing as an “approximate deduction;” the conclusion of a deduction will always be true since its premises are also true.
Deductive inferences are more easily identifiable in puzzles formulated in natural language. For example, the following brain teaser (no. 029) in Professor Layton and the Curious Village.
Five suspects are called into police headquarters for questioning. They give the following statements:
A: “One of the five of us is lying.”
B: “Two of the five of us are lying.”
C: “I know these guys, and three of the five of us are lying.”
D: “Don’t listen to a word they say. Out of the five of us, four are lying.”
E: “All five of us are dirty rotten liars!”The police only want to release the suspects who are telling the truth. How many people should they let go?
If, when thinking about the question above, you chose person D, that’s right! If it wasn’t just a guess, you probably just made a deductive inference.
The premises are as follows:
- There are only five suspects (A, B, C, D, E) in a crime;
- Each suspect accused, within the group defined in 1, a different number of liars (respectively, from one to five);
- There is at least one suspect who is speaking the truth.
Now, we can reason deductively by hypothesis, noting which hypotheses lead to an absurd (contradictory) conclusion.
If A speaks the truth, someone is lying. Who? In this scenario, person E needs to be a liar, because if he spoke the truth, A would also be lying. But D must also be lying, because if he spoke the truth, then there would be four liars, which should include either A or E. Therefore, if there is more than one liar, this contradicts A’s claim, which, therefore, cannot be telling the truth.
Following this hypothetical method for reductio ad absurdum (lat.), it will soon be discovered that
- the only one who may be speaking the truth is suspect D.
In other words, given that premises 1, 2, and 3 are true, it is impossible for the above conclusion to be false. Similar to this example, there are also graphic puzzles that use deductive reasoning, and with many variations of its application.
And in other cases, in games such as Minesweeper, for example, although the player will also need luck in many of his moves, he may also use deduction to conclude from time to time that there is undoubtedly a mine in a given space on the field.
But there are also cases where the player does not need luck (Baba is You is an example), but in some games, the player is also required some reaction time skills. This is the case with the classic Lemmings, where you need to use some of your units to redirect the others to a safe path.
In some cases, there are deductive action puzzles that emphasize the physical challenge of reaction time far more than the mental challenge of solving logical problems, like the classic Tetris.
Linear and non-linear logic puzzles
It should be noted that, in the case of Lemmings and Tetris, there are different ways to solve the puzzles. All of these solutions, however, can be deduced by the premises of the mechanics of the game and its level design.
The Witness is a good example of a game in which different ways of solving a puzzle deductively are very clear.
To use Josh Bycer’s conceptual differentiation, we can say that puzzles like the one mentioned in Professor Layton and the Curious Village are linear puzzles, while the puzzle above in The Witness is an instance of a non-linear puzzle.
However, non-linear deductive puzzles can still be subdivided into two types: those focused on discovering solutions and those focused on inventing them. This duality between the emphasis on discovery, on the one hand, and invention, on the other, has been well explained by Mark Browm.
In other words, there are those puzzles that, despite having multiple answers defined for a problem, are discovered by the player (this is the case in The Witness), but there are also puzzle games that just provide tools for the player himself to build a solution to the problem. This second type of non-linear puzzle is present in coding games.
Coding games are games specialized in programming, that is, in the construction of algorithms for specific tasks. These games, however, can simulate explicit programming (as in Human Resource Machine), but coding games can also simulate it implicitly through more diverse mechanics. For example, involving physical and chemical variables in Infinifactory and SpaceChem, respectively.
These games, despite not working directly with a code like Human Resource Machine does, still requires the player to develop a set of steps to be followed automatically.
Note that the situation of all these games is different from that of previous puzzle games, and even that of World of Goo, where the player himself needs to perform his reasoning step by step.
But non-linear puzzles, in general, have in common the possibility of discovering or creating more or less economical solutions. It is common in games of this style to demand the player to discover or create solutions that are as economical (in number of steps or actions) as possible.
But we must not forget that several puzzle games do not require much logical reasoning, at least not from traditional logical reasoning — the one related to deductive reasoning. Instead, many (and perhaps most) puzzles are focused on induction or abduction, as we will see below.
Inductive Puzzles (Trial-and-Error/Exploration)
Unlike deduction, induction is a reasoning process based on experimentation and provisional generalizations, so that the conclusions of induction are always fallible. In this sense, even if a good inductive inference results in a conclusion that works most of the time, it is common that a context is found in which the premises of induction are true and, even so, its conclusion is false.
A puzzle can be considered an inductive or trial-and-error puzzle when it is based on experimenting with mechanisms or objects around the puzzle before solving it, also requiring guesswork, observation, verification, and exploration to better understand it.
Probably the two main puzzle subgenres in this style are puzzle platform and puzzle adventure.
Puzzle-platformers like Fez and Limbo are rich in exploration elements. In both games, the player needs to observe the surrounding space well and experience his hypotheses in real time through the mechanics that the game provides, such as jumping or using certain objects and mechanisms.
Similarly, puzzle adventures with point-and-click mechanics, such as Gorogoa, Myst and Machinarium, also require the player to explore the scene well and infer where to click or what item to use on a given occasion.
In both cases, puzzle platformers and puzzle adventures are offering problems that can be solved by inductive methods, such as pure trial and error or sample generalizations.
In Gorogoa, for example, we can partially and totally solve some of your point-and-click puzzles in the “brute force” of trial and error, simply clicking on random places in the image until one of the objects turns out to be interactive and useful. However, over time, in Gorogoa, as well as Limbo, Machinarium, and other games, we can formulate generalizations about what is possible to interact with, what is its function, and what is not or is useless to solve a certain problem.
In this sense, inductive puzzle games can become progressively more predictable and easier, if the developers are not constantly bringing new objects, functions, mechanisms, and scenarios in (making it so players cannot rely on the generalizations they made previously and need to start a new process of exploration). Something similar occurs with abductive puzzles.
Abductive Puzzles (Investigation)
Some logicians consider abduction, for good reason, as a specific type of induction. But I chose to explain it separately in this topic since its use in puzzle design results in a very different experience in gameplay.
As in the examples of inductive puzzles above, the conclusions inferred from abduction are always provisional, and can also be based on background generalizations. However, abductions do not involve the experimental method of trial-and-error and have a certain peculiarity.
Abduction is reasoning used to investigate a phenomenon in order to infer which is the most plausible conclusion about what happened at a given time and space or what caused it.
Abductions are widely used in games in which the player impersonates a detective, an archaeologist, a lawyer, or any other character who fulfills the role of investigator in a crime, case of mystery, etc. Thus, this kind of reasoning is very present in adventure games that involve the investigation of criminal cases. Disco Elysium and Ace Attorney series are good examples.
But an excellent example of a puzzle game that requires a lot of abductive reasoning is Return of the Obra Dinn. In this game, the player takes on the role of an agent for the British East India Company to investigate what happened to the crew of the Obra Dinn, a merchant ship missing for five years, after it reappeared off the coast of England with no one alive aboard.
For his investigation, the player has a watch that, when facing a corpse, has the ability to show the player the last moments of the dead person’s life. As it is not possible to interact in the victim’s past, to arrive at the conclusion of who the crew member was, who killed him, and in what way he killed, a lot of abduction and, occasionally, deduction is used.
For example: let say there is a corpse that was found alone on the other side of a wooden wall, on the outside of the ship. Then, when you visit the last moments of his life, you hear a shot from a firearm against the wall and see that the one who fired it was another sailor on the other side of the wall (inside the ship). By abduction, you can conclude that the most plausible thing is that the victim died shot by another sailor who unintentionally killed him.
Note, however, that this is not a deduction, as the premises extracted from his observation and hearing do not guarantee that the victim died in this way: the victim could have died of something other than the projectile (no autopsy was done), and the sailor could have intentionally killed the other sailer (somehow, he could have known the victim would be there at the time).
Of course, these assumptions above are less plausible, but not impossible. And distinguishing more plausible scenarios to explain a phenomenon is precisely what characterizes abductive reasoning.
Joining different kinds of reasoning in puzzle design
Although it is possible to classify many puzzle games that require more deduction, others that require more induction, and even others that require more abduction, we must not forget that most puzzle games mix, at least a little bit, different kinds of reasoning.
In Braid, for instance, there is a certain moment where you need to solve a deductive problem, but it presupposes using an illustrated platform inside a puzzle piece to be able to reach another one, but at no time was that explained to you. You need to find out by experimenting by induction. Similarly, in The Talos Principle, the player will need to learn, by induction, how the tools at his disposal work and only then deduce how to solve the puzzles.
When it comes to mixing different kinds of reasoning, perhaps the most interesting cases are that of puzzle designs that result in what I call “complete puzzle games.”
A complete puzzle game can be defined as a game in which not only its problems ,but also its narrative and even its mechanics must always be discovered by inferences (by deduction, induction, or abduction). A notable example is The Witness.
Obviously, as with all previous categories, The Witness is not the only example in that category (Myst, Baba is You and many others could also be cited), but I will use this Jonathan Blow game to explain the concept.
Although there are deductive solutions to the problems posed in the world of The Witness, no game mechanics are explained to the player. It is necessary to discover, by induction, what the symbols mean to solve the puzzle and also find out which elements of the scenario are relevant to use as a premise in a deduction.
As for the plot of The Witness, it is also not explicitly explained by any text or speech. Everything needs to be inferred by the player’s reasoning, usually by abduction. As an example, when arriving in a city where its inhabitants are petrified, it is possible to infer, by abduction, the activity that one of them was engaged in just by observing their shadow and some stones on the ground.
In all ways of puzzle design, puzzle games have great potential to develop the three kinds of human reasoning (deduction, induction, and abduction).
I also see great creative potential in games of this genre, sometimes even reaching creative genius. Complete puzzle games are especially interesting, as they are able to immerse the player in a world of complete mystery, a world that consists of a major problem to be solved and that can only understand it by its own intellectual effort.
Surely this genre will continue to offer us many mysteries to investigate, mechanics to test, and problems to solve. And I’m always looking forward to unraveling them all.
