The goal of this sequence is to explore how to **use algebra strategically**. That's the essential skill set this course is designed to strengthen, whether you're brand-new to algebra or already planning to major in mathematics.

The first three challenges in this sequence are warm-ups, but the last two are much trickier.

If you arrange all five of the tiles below to make the statements in both boxes true, **which box must the tile "3" be in?**

*Note:* **Product** is the result of multiplication.

**When you're finished, which tile is in the same box as 5?**

**What is the highest-numbered tile in Bai’s box?**

This course covers traditional logic, algebra, and number theory techniques, but the problems are also designed to push your mathematical strategy to the next level. You're learning to approach complex problems creatively, *not* just learning how to apply rote techniques.

You only learn deeply when you're challenged to think for yourself and exercise your brain by solving hard problems!

These last two challenges are particularly tricky.

If you arrange all eight of the tiles below to make all of the claims true, **what is Damon's highest-numbered tile?**

**Who has the tile numbered 5?**

**really made you think** and strengthen the skills you used to strategically apply the information provided. If it did, then consider this a success!