# 📖 Algebra

The mathematical relation of numbers of symbols

Alegebra is about symbols and the manipulation of symbols. On puzzle pieces, it mostly encodes a value the player must find.

In puzzle games we are mostly limited to elementary algebra, which uses basic equations and a few symbols. For example:

• x + 3 = 10

Where `x` is the unknown we wish to find. Through a series of steps we can work out that `x = 7`.

Live Examples:

#### Graphical Replacement

On puzzle pieces, algebra is often hidden behind uncommon symbols. Often the numbers are replaced with symbols, either generic or real-world objects. For example:

• 🎂 = 🥚 + 🚰

The player needs to discover the value of 🎂. The value for 🥚 and 🚰 can be found on other puzzle pieces. Often those values maybe further obscured: perhaps the number of eggs in the room has to be counted, and the amount of water in a bucket measured.

When the values are further abstracted, we tend to find only the most elementary of algebraic expressions. Combined many layers of puzzles can quickly ramp up the difficulty.

#### Simultaneous Equations

Several puzzles involve numerous equations that must be combined to arrive at the final value.

• x + 3 = y
• y - 4 = z
• z = 5

This provides a mean to distribute the puzzle over multiple pieces.

It also allows another way to introduce new symbols. The above could be rewritten as:

• ☿ + 3 = ♀
• ♀ - 4 = ♂
• ♂ = 5

Where the player needs to find the god of Mars ♂ to determine the value of Mercurry ☿. The use of symbols allows algebra to fit into the theme of the game — if only in an aesthetic nature.

### Generic Math Puzzles

Algebra puzzles are a type of math puzzle, though non-algebraic puzzles exist. Additionally, if a puzzle involves math, but the focus isn't on finding the unknowns, we may not call it an algebra puzzle.

If simple enough, an algebra puzzle may be referred to as a counting puzzle.

#### Feedback on Working Draft

If you have any questions, need an example, or want clarification, then let me know. Ask on Discord or Twitter.

Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.