The Wednesday Morning Math Challenge: Week 1

One of my life’s passions is the desire to learn about the unknown — and to expand our understanding of it. For the rest of the NFL season, I’ll be sharing that passion with you.

Each week I’ll give you three puzzles. Sometimes they will involve math, other times logic and some of them will test your spatial awareness and reasoning. What unifies every one of these problems is that each one will make you think.

Give the problems below a try, and check back next week for the answers — and a brand new set of puzzles.

1. A number is said to be a perfect square if it can be written as an integer squared, and a perfect cube if it can be written as an integer cubed. For example, four is a perfect square (2²), and eight is a perfect cube (2³). The number one is both a perfect square and a perfect cube. What’s the next smallest number that is both a perfect square and perfect cube?

2. Two cars 60 miles apart are traveling 15 mph directly toward each other. Between them is a bee, flying back and forth between the two cars at a speed of 32 mph. By the time the two cars meet, how far will the bee have traveled?

3. Suppose you have an eight-by-eight grid (like a checkerboard) and eight pebbles. Is there a way to place the pebbles so that no two share the same column, row or diagonal? If so, can you give an example?