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Martin Gardner's Best Math Puzzles (Part 1)

If you’re into math and logic puzzles, you've probably heard of Martin Gardner. And if you’re not into those kinds of puzzles, you should be! Math Dude highlights some of this math master's best teasers, for both novices and experts.

By
Jason Marshall, PhD
Episode #219

Martin Gardner was a once-in-a-century kind of guy. If you aren’t familiar with his prolific writing—and in particular, his amazing collection of math and logic puzzles—well, you really should be. I own at least a dozen books authored by Martin Gardner, and each and every one of them is a true treasure.

When Mr. Gardner passed away in 2010, he left math fans of the world with enough material to keep us entertained and educated for at least two lifetimes. As part of the celebration of the 100th anniversary of his birth, Scientific American has put together a wonderful Martin Gardner tribute page where you can find out much more about his life and work.

I encourage you to check it out right away.

As part of my own tribute, I’m going to feature some of Mr. Gardner’s best-known puzzles from his book My Best Mathematical and Logic Puzzles, in both this and future episodes. Martin Gardner’s puzzles span a huge range of styles and subjects, and to give you a taste of what you have in store once you dive into his world, today we’re going to take a look at three of them..

Puzzle #1: The Returning Explorer

The very first puzzle in Martin Gardner’s book, My Best Mathematical and Logic Puzzles, is called “The Returning Explorer.” We talked about a similar puzzle back in the Math Dude episode Advice for New College Grads - How to Use Math to Land Your Dream Job. Here’s how Mr. Gardner poses this puzzle:

“An explorer walks one mile due south, turns and walks one mile due east, turns again and walks one mile due north. He finds himself back where he started. He shoots a bear. What color is the bear? The time-honored answer is 'White,’ because the explorer must have started at the North Pole.”

Before we continue with Mr. Gardner’s exposition, do you understand why the North Pole is an answer to this puzzle? If you imagine standing at Earth’s North Pole, you’ll find that any direction you walk is south. So walking one mile south (which means any direction), then one mile east, then one mile north lands you right back where you started from.

Mr. Gardner goes on to write, “But not long ago, someone made the discovery that the North Pole is not the only starting point that satisfies the given conditions! Can you think of any other spot on the globe from which one could walk a mile south, a mile east, a mile north, and find himself back at his original location?"

Take a minute and try to come up with another possibility, then come back when you’re ready for the answer...