Mathematical Fundamentals

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.

Challenge Set

               

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

Challenge Set

               

Arrange the six tiles below to make the statements in all three boxes true. When you're finished, which tile is in same box as 5?

Challenge Set

               

Ankit and Bai have split up a set of tiles numbered 1 through 6. What is the highest numbered tile in Bai’s box?

Challenge Set

               

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!

Challenge Set

               

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?

Challenge Set

               

Hana, Ivan, and Jackson have divided up a set of tiles numbered 1 through 9. Who has the tile numbered 5?

Challenge Set

               

We hope that at least one puzzle or solution in this course's introduction really made you think and strengthen the skills you used to strategically apply the information provided. If it did, then consider this a success!

Challenge Set

               
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