During Chapter 5 when you visit the Thunder Plains you'll go through a series of events that opens up a secret cave. Before you can do much with the cave you must rescue Cid and fight the Machina Panzer. Once that is accomplished this mini-game becomes available. The dungeon you rescued Cid from is really a huge puzzle. To solve it, ideally, you'll need a pen and paper (possibly a calculator) and a Charm Bangle. The puzzle can be solved without the Charm Bangle (they're only dropped in two boss battles and as a first place prize in Blitzball so it's possible to miss this accessory), but things become much easier with the bangle equipped.

Upon entering the dungeon a brief explanation of the puzzle is given. Then the first number you'll need is flashed in the lower-right corner. The yellow number is the door this number goes to and the white number is your first key number. In order to open doors in this maze you'll need to add two key numbers together. After this first set of numbers is shown to you two chests will appear in front of you. You can only choose to open one of the chests. They will either give you a hint, open the next door, or do nothing.

After you see the key number a red arrow on the map will guide you to the door the number goes to. When you get to the door you'll need to examine it to get the second key number (upper left corner). After that you'll get the next key number and door (bottom right corner). Now you'll need add the two numbers for this door together and input the result into the door. (Make sure you write down the sum and door number for each door.) If you're right it will open. You'll then get to select from two chests again. If you do happen to open the next door then the code you would have entered in is shown on screen.

There are various forms the key numbers will take. Sometimes it's a math problem. Sometimes they won't even be an integer. Instead it will say something like "Amount of gil earned between entery and door 7" or "Number of battles since entry". That's where the Charm Bangle comes in handy - because you won't have any random encounters the answers to those two questions will always be 0. If you don't have the accessory it is possible to solve the puzzle, but you'll have to track the number of battles and amount of gil. You'll will have some help in this because there are 3 special walls in the maze. In the northeast corner the wall keeps track of how much gil you've earned from random battles. The southeast corner wall keeps track of all the codes for every door you've opened so far. Finally the wall in the Southwest corner keeps track of the number of random battles fought since opening each door. However, remember that once you write down the numbers at the walls you will still have to keep track of everything between the special wall and the next door (if you don't have a Charm Bangle).

There are 16 doors in this dungeon and as you go through each of them you will come across item chests. One of the last ones you find contains Paine's Corpus Invictus. Now, once you've made it through the dungeon once you'll have satisfied the completion points requirement for solving the dungeon. However, to get everything from this cave you'll need to exit, reenter, and solve the puzzle again. When you do a chest will appear in the north hallway. It contains the Force of Nature accessory.