Welcome to Math Towers!

Let's cover the basics. Math towers is a deduction game. The goal is to quickly figure out which section doesn't belong and remove it. What is a section?

The image above shows you the focus point of the game. In the easiest mode, a crane lowers a new floor that contains three sections. The tower below it is only two sections wide. You must remove a section. So how do you know which to remove?

The rules are simple. After you remove a section, the remaining sections must add up to the current floor number. For example, in the picture above, there are three sections with values 4, 0 and 6. The sum of these floors needs to add up to the current floor number, which is 6. The only way to achieve this is to remove the section with value of 4. The two remaining sections have values of 0 and 6 which sum to 6.

Sometimes there will be more than one right answer. Don't worry about it. The rule is that once a section is removed, the remaining sections must sum to the floor number. No matter which you remove, as long as that rule is met, it will count as a successful selection. For example in the image below, either 4 can be removed.

Time Limit

To keep things interesting (and hopefully calculator free), there is a time limit for each floor. The time limit is 5 seconds in the easiest mode. This limit does increase in harder modes. If you don't make a selection before the time limit is reached, the floor will be left unfinished and the next floor will be brought down.

Unfinished Floors

Whenever you select an incorrect section, or run out of time on the current floor, the floor is left unfinished and a new floor is brought down.

Checkpoints

The game starts out with the first five floors completed for you. Every 25th floor is a checkpoint. Once you reach this checkpoint, any future games will start from this checkpoint.

One other note: checkpoints are unique per game mode and difficulty. So for example if you get to floor 125 in addition and then switch to division, you'll have the opportunity to start back down at the easier levels to get your division brain muscles warmed up.

Game Over

The tower can support up to five unfinished floors. Once a sixth floor is left unfinished, the tower will collapse and the game is over. If you made it to a checkpoint then when you start a new game it will start from that checkpoint.

The rule makes sure you are maintaining at least an 80% average between checkpoints. A modest goal.

Starting and Stopping the Game

When the game loads it automatically starts and waits for your first selection. To stop the game press the red square button

To start a new game, press the green play button.

Game Modes

Addition is fun, but so are other math operations. This game supports addition, subtraction, multiplication, division and modulo arithmetic. To change game modes, you can click the button at the top right of the screen.

One thing to keep in mind that the order of operations is important in some modes.

In addition 2 + 4 is the same as 4 + 2.

In subtraction 2 - 4 is not the same as 4 - 2.

Subtraction

In subtraction, the goal is similar. Once a section is removed, the difference of the two remaining sections must equal the floor number. In this example, there are three sections you can click. Lets examine each option.

Remove section 1

You are left with 7 and 1.
7 - 1 = 6.
Great! This is the right answer. Lets look at the others to see why they would be wrong.

Remove section 2

You are left with 6 and 1.
6 - 1 = 5.
This doesn't equal the floor number.

Remove section 3

You are left with 6 and 7. 

6 - 7 = -1. 

This also doesn't equal the floor number.

Multiplication

Hopefully rules are getting clearer. In this example you have to remove a section. We'll go over the options again.

Remove section 1

You are left with 3 and 1.
3 x 1 = 3.
This doesn't equal the floor number.

Remove section 2

You are left with 2 and 1.
2 x 1 = 2.
That doesn't quite work either.

Remove section 3

You are left with 2 and 3. 

2 x 3 = 6. 

Cool. This equals the floor number.

One other thing you may note here. 2 x 3 x 1 = 6 as well. Still, you have to remove a section, and in this case there is only one that can be removed.

Division

Remove section 1

You are left with 9 and 3.
9 / 3 = 3.
This doesn't equal the floor number.

Remove section 2

You are left with 18 and 3.
18 / 3 = 6.
This equals the floor number and is the right answer.

Remove section 3

You are left with 18 and 9. 

18 / 9 = 2. 

Modulo

This is probably the most challenging game mode for people who aren't familiar with modular arithmetic. 

I'm not going to paste a formal definition of modular arithmetic. The easiest way to think of it is as the remainder of a division. The modulo operator is the percent symbol "%".

5 % 2 = 1. Why? Think in terms of division and remainders. 5 divided by 2 equals 2 with a remainder of 1.

38 % 10 = 8. 38 divided by 10 equals 3 with a remainder of 8.

Modular arithmetic is concerned with the remainders of a division.

In the example above, we need to figure out which section to remove

Remove section 1

You are left with 8 and 9.
8 % 9 = 8.
(8 divided by 9 = 0 with a remainder of 8)

Remove section 2

You are left with 33 and 9.
33 % 9 = 6.
(33 divided by 9 = 3 with a remainder of 6)
Cool. This equals the floor number.

Remove section 3

You are left with 33 and 8. 

33 % 8 = 1. 

(33 divided by 8 = 4 with a remainder of 1) 

Difficulty Levels

To make things more difficult, you can increase the number of sections per floor. An expand gesture will increase the number of sections, and a pinch gesture will decrease the number of sections.

Changing the difficulty can be done at the start of the game, after pressing the play button but before starting the actual game play (before tapping a section). 

The time limit per floor increases with the difficulty.

And that's the game.