These criticisms are all true, but let me defend myself before we dive in: Though this challenge is arguably a parent to the other challenge types, I am attempting to highlight a particular slice of the challenge that is meaningful in modern game design analysis and discussion. It's nature as a super challenge is why I saved it for last, but in certain genres it is overwhelmingly present and distinct from the other three types of challenge.
Can you guess what it is from that set up? Probably not.
The last challenge type is the Logic Challenge! What's a logic challenge? I'm glad you asked!
A Logic Challenge is any challenge that requires the manipulation of a set of axioms and principles to find a valid solution.
This challenge is fairly self explanatory. A logic challenge can be thought of as either a proof, or more importantly and equivalently, a math problem. As I noted above, the astute reader will shout that all other challenges are logical challenges. Spatial challenges require a solution to a more real time representation of "If a train leaves Albuquerque at 1,000 miles per hour and another train leaves kalamazoo at 5,000 miles per hour when and where will they meet if both trains can tunnel through moutain ranges and fly over the ocean?". It's true, but for my purposes logic puzzles are meaningfully distinct in that they involve the willful manipulation of numbers and rules.
My example for this will draw on the Shin Megami Tensei series, a hardcore RPG series that's almost older and certainly deeper and absolutely more intense than any other RPG series I've heard of. The first, and most prominent application of this challenge in the SMT series, is simply that it's a traditional turn based RPG.
All RPGs (at least, the old school ones before action got involved...not including Zelda 2), are about statistics. Characters have their resources (challenge type number 3!), but they also have an attack, defense, speed, and whatever other stats the developers included. Playing an RPG is tackling the interplay between the stats of your characters, and the stats of the opponent. If I have an attack rating of 70, and the dragon I'm about to take on has a defense rating of 5000, I need to crunch the numbers (as trivial as they are in this example) to realize that I am far too weak to take on the dragon. Obviously in most RPGs, these calculations are much greyer (for one thing, you usually don't know your opponent's defense rating), which is half the fun (I think), but that's beside the point.
The real meat of a logical challenge is manipulating rules. Number crunching is a (complicated) extension of this point, but rule manipulation is demonstrated beautifully in SMT. In several of the Shin Megami Tensei games, each character has an elemental affinity, and along side that, there are several elemental spells and attacks. By attacking a character with an attack that belongs to the opposite elemental affinity, the effects of your attack are greatly modified.
This is really what logic challenges are all about: It's a question of, this rule states that if I use this command (say a fire spell), against you (you're an ice demon), my chances of success are greatly increased (because I deal double damage). As I stated before, it's not hard to argue that this is true for all challenges, but this is a significant distinction, particularly in the case of RPGs.
The real meat of a logical challenge is manipulating rules. Number crunching is a (complicated) extension of this point, but rule manipulation is demonstrated beautifully in SMT. In several of the Shin Megami Tensei games, each character has an elemental affinity, and along side that, there are several elemental spells and attacks. By attacking a character with an attack that belongs to the opposite elemental affinity, the effects of your attack are greatly modified.
This is really what logic challenges are all about: It's a question of, this rule states that if I use this command (say a fire spell), against you (you're an ice demon), my chances of success are greatly increased (because I deal double damage). As I stated before, it's not hard to argue that this is true for all challenges, but this is a significant distinction, particularly in the case of RPGs.
I suppose a big application of this challenge for me is essentially arbitrary laws that modify a more intuitive rule set. Another great example of this is Final Fantasy Tactics Advance. In FFTA, there are rules governing battles, like "no Swords", which change over a set interval (oh look, a timing challenge!) which you can plan around. This is sort of where the lines get blurred on challenge types, but that's okay.
In my experience, logical challenges add a lot of richness to gameplay for advanced players but increase the barrier to entry for beginners substantially. As a result, I think it's fair to say that the more rules you enforce on the player, the higher the difficulty. Though I think it's worth also mentioning that the effect of the rules is important too. If SMT's elemental system offered modest gains in damage (like Final Fantasy games), but nothing crucial to victory, then nobody feels put off by not understanding the systems in place.
