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# Algebra Through Puzzles

Supercharge your algebra intuition and problem solving skills with these fun puzzles!

How much does a single red square weigh?

This Exploration investigates how the logic you intuitively apply when solving puzzles mirrors fundamental algebraic strategies.

**The goal is to help you become a stronger problem solver!**

To do so, we will teach you new mathematical techniques and push you to recognize and generalize the algebraic techniques that you already intuitively use as you problem-solve.

- A full jar of honey weighs 1000 grams.
- With half of the honey, the total weight is 600 grams.

**What is the weight of the empty jar in grams?**

What weight will the fourth scale display?

Think carefully! There's a quick and clever shortcut for solving this.

At the end of this Exploration, you'll have a thorough toolbox of algebraic techniques that feel natural to use and empower you to master complex problems and puzzles!

**How many green squares should be placed on the right side of the bottom scale in order to make it balance when released?**

We’ll also delve into some applications of algebra in physics!

**Which way will the balance above tilt if released?**

How to Solve Leverage Puzzles:

Archimedes once said:

*“Give me a place to stand and with a lever I will move the whole world.”*

His claim was in reference to the fact that the amount of force exerted on a lever arm is equal to the weight of the object sitting on it multiplied by the distance of that object from the fulcrum of the lever: \[\text{Force} = \text{Weight} \times \text{Distance from Fulcrum}.\] This equation explains why the lever system below is balanced, even though there’s a rock on one side and only a small bird on the other: \(120 \times 1 = 40 \times 3.\)

And, at least in theory, if there were a force pulling the earth and Archimedes both "down" and something fixing the position of the fulcrum in space...

(Yes, Archimedes would also need a space suit.)

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