Welcome to “Inside the Guide”, the column that gives you a behind-the-scenes look at writing videogame walkthroughs. This month, I decided to tackle the game *Garfield Tycoon* for iOS. In this game, just like in real life, *Garfield* openly attempts to make a fortune through aggressive merchandising.

The goal of *Garfield Tycoon* is to build a 100-story building. Like most freemium games, it starts off easy, then it develops a steep difficulty curve. You can only get about five levels in before you need to stop and grind for Garfield coins. I took careful notes while playing the game, and I got these results:

- Floor 3 costs 6,75 coins and is built in 1 minute.
- Floor 4 costs 1,200 coins and is built in 2 minutes.
- Floor 5 costs 1,875 coins and is built in 3 minutes.
- Floor 6 costs 2,700 coins and is built in 5 minutes.
- Floor 7 costs 3,675 coins and is built in 8 minutes.
- Floor 8 costs 4,800 coins and is built in 13 minutes.
- Floor 9 costs 6,075 coins and is built in 21 minutes.
- Floor 10 costs 7,500 coins and is built in 34 minutes.
- Floor 11 costs 9,075 coins and is built in 55 minutes.
- Floor 12 costs 10,800 coins and is built in 89 minutes.

How much items cost is useful information to include in a walkthrough, but this is pushing the limits of how far you can go without spending money or doing a lot of waiting. Am I really going to play this game the whole way through in order to get the statistics on all 100 floors? No way! There must be an easier way to figure it out!

It turns out that the time it takes to build each floor is not random. 1, 2, 3, 5, 8, 13, 21, 34, etc. is a mathematical sequence known as the Fibonacci sequence. Here’s how it works: you add the two previous numbers together to get the next number. I have no idea *why* they decided to use this sequence for a *Garfield* game, but I’m not complaining. I can easily copy/paste this info from a mathematics website and put it in my guide.

Since the timer follows a sequence, I guessed the prices do, too. After all, they *look* like some sort of pattern. I couldn’t figure out the pattern by looking at the numbers, so I decided to try a strategy I call “odd numbers are difficult, so I’m gonna pretend they don’t exist”:

- Floor 4 costs 1,200 coins. That’s 300 times 4.
- Floor 6 costs 2,700 coins. That’s 300 times 9.
- Floor 8 costs 4,800 coins. That’s 300 times 16.
- Floor 10 costs 7,500 coins. That’s 300 times 25.
- Floor 12 costs 10,800 coins. That’s 300 times 36.

Oh snap, looks like I found the regular pattern! It looks like they’re working off of square numbers. In particular, it looks like they take the floor number, divide it in half, square it, then multiply it by 300. The simplified form of the equation is 75x^{2}, where x is the floor number.

Now that I know the regular patterns the game follows, I can give information that goes all the way up to level 100, without going past level 12. Nice!

I filled out a thorough chart for the game, but then I stopped a third of the way through when I realized I made a mistake somewhere. The waiting time for the lower floors doesn’t look so bad, but it quickly gets out of hand. As in, the number of minutes you have to wait for Floor 30 is over a year. And anything past Floor 39 takes over a century.

Since the in-game timer only has four digits, I’m going to hope 9,999 minutes is the upper limit. You’ll reach that at floor 20, which is 1/5 through the game. It’s a little over four days, which is not *that* bad, but still. This game is really pushing the strategy of “include long waiting times, so people will pay to skip them”.

But just to cover my bases, I added a little disclaimer to my guide, saying I haven’t beaten the game all the way through. And…that’s basically it! My walkthrough work this month was mostly made up of math. Thanks a lot, Garfield.

As an addendum to this article, it looks like the game developers ALSO realized the waiting time system was out of control and would soon go up by hundreds of minutes with every level. To avoid this, they made it so the timer only goes up by 16 minutes per level, starting on Level 15.