Musical challenges test your ability to recognize and recall musical pitches, tones, and rhythms.
Consider Loom. Its gameplay centers on music so much so that all interactions come in the form of four-note sequences called drafts. As you play the game, you learn drafts by observing objects that have qualities of a relevant draft. For example, you learn the "sharpening" draft by watching a blade while it is being sharpened. Normally when this happens, your distaff -- a tool used for spell weaving -- glows with the appropriate note. However, if you play as an "expert" then your distaff is not marked and you must play solely by ear, demanding an even stronger understanding of pitch and tone.
In the same manner, the Selenitic Age in Myst with its trickling waterfalls, whistling winds, fiery chasms, and the sound of wind whistling through crystalline formations requires you to recognize audial patterns. Most notable and probably misunderstood, is the vast maze in the underground caverns of the Age, which is traversed with what is known as the Mazerunner.
When you first sit down in its pilot chair, it looks simple enough: a FORWARD button, a BACKTRACK button, a LEFT button, a RIGHT button, and a compass. By pressing FORWARD, the runner is lowered onto a track and a small bell sounds – ping. After some trial-and-error (or by recalling the tones from the Mechanical Age), you can learn that sound is a cue corresponding to a compass heading.
In fact, each direction has an associated sound: "ping" means north; "chirp" means west; "spring" means east; "dong" means south. Knowing this, you can easily travel the caverns by following the cues at each intersection. Although this task does have you traversing a maze, your ability to recognize the musical patterns circumvents any need to map the space.
Interpersonal challenges test your ability to understand the intentions, motivations, and desires of other people. They involve reading people and changing your approach to achieve a desired goal. While being extroverted or liking other people may be beneficial, it is certainly not a requirement.
Take poker, for example. The most successful players aren't masters at calculating probabilities. Instead, they are able to read their opponents, noticing the slightest nonverbal gestures and inferring their feelings about their hands. If you closely look at your opponents when they first look at their hands, most won't be able to hide their excitement or disappointment. Or if there are sudden changes in their behavior for a hand (e.g. somebody who is normally very talkative suddenly becomes quiet), you know something is going on. Once you get a good read on someone you'll know when to cut your losses or play aggressively.
In the same way, interrogation in L.A. Noire tests your ability to read people. By asking something compromising, you determine whether the suspect is telling you the truth or lying. Some notable tells are sweating, shifting eyes, and nervous tics. Being able to correctly read the suspect's behavior leads you closer to the truth, while any misunderstandings cause the suspect to either provide bad or no information.
Do note that interpersonal challenges require engaging people at a social level. If you're interacting with others as though they're cogs in a machine, then you understand them as elements in a causal system. Additionally, these challenges are different from the pleasure felt when playing with or against other people. Challenges require overcoming obstacles; in this case, the obstacles are people.
Intrapersonal challenges test your level of self-awareness. They deal with your capacity to understand your feelings, opinions, fears, experiences, preferences and motivations. In effect, you are the challenge.
One game that masterfully uses intrapersonal challenge is the experimental game Brainball. In the game, you and your opponent compete to control a ball's movement across a table. To do so, the two of you each wear a strap containing electrodes around your foreheads. The electrodes read alpha and theta waves generated when you are calm and relaxed, which move the ball forward. So in order to win, you need to be relaxed and focused. Conversely, if you are stressed, you will lose.
To a lesser extent, the same can be said about games like Resident Evil and Silent Hill. These games can make your heart race, mouth dry, and palms sweat. Consider the first time you stumble across the pale, overtly muscular figure with a large red, triangular head in Silent Hill 2. The ghastly scene is completely unexpected as you witness it rape and murder two mannequins from a nearby closet. What the hell is this thing? Are you trapped? Are you safe? At its core, you are challenged to overcome your fear and understand the situation at hand.
Naturalistic challenges test your ability to recognize and categorize both natural and unnatural artifacts.
Let's take the game Peekaboom [pdf link] by way of example. The game involves two random players taking different roles in the game: Peek and Boom. Peek starts out with a black screen; Boom starts with an image and a word related to it (see the screen below.)
Your goal, as Boom, is to slowly reveal portions of the image so that Peek can guess the related word. For example, if the image contains a cow and a field, and the word associated to the image is "cow," then you reveal only the parts of the image that contain the cow. Both you and Peek need to understand what characteristics constitute any particular artifact in order to succeed.
Contrary to its namesake, naturalistic challenges do not always involve identifying natural artifacts. For instance, in Shivers II, a series of numbers is revealed after holding a finger-printed piece of paper to a flame: 5559547. What is it? A safe combination? A password? The number is meaningless. You may stare blankly at this number not knowing what to do – I did.
Yet if it were written as 555-9547, it's immediately clear that it's a phone number. Until that leap, the number is just random noise. Now you may have recognized the number as a phone number even without the hyphen. But ask yourself, would you have recognized so quickly if it were written as "five million five hundred fifty-nine thousand five hundred forty-seven"?
These challenges should not be confused with lock-and-key causal systems. When you pick up the mechanical nightingale in King's Quest VI, you may not understand how it interacts with the space -- other than it sings -- but you know that it is a mechanical nightingale. Understanding how an artifact and its interactions affect the space and understanding what the artifact actually is are distinctly different challenges.