The writer and puzzle master Martin Gardner, who died in 2010, was once said to have turned dozens of innocent youngsters into maths professors – and thousands of maths professors into innocent youngsters. Maths writer Colm Mulcahy looks back at the amazing career of a man who would have been 100 this week.
Let’s warm up with three gems from the vaults:
1. What angle is made by the two red lines drawn on the two sides of the cube, as shown in the illustration?
2. A logician visits a distant planet inhabited by two groups of aliens, compulsive liars and faithful truth-tellers. She comes to a fork in a road – one road goes to the left, the other to the right. She meets two aliens there, one a liar, the other a truth-teller… but she doesn’t know which is which. The logician must ask just one Yes/No question to discover which road she should take to reach their leader. She thinks for a moment and then asks her question. What question might she have asked?
3. Imagine heating a metal ring enough so it expands. What happens to the hole, does it get bigger or smaller?
You may already know the answers to the above questions if you’ve read some of the 100 or so books written by the American man of letters and numbers, Martin Gardner (1914-2010). His works have long been popular with a variety of people, from science and maths types, to lovers of magic, enemies of pseudoscience, and aficionados of Lewis Carroll – Gardner’s Annotated Alice, by far his best seller, has sold more than a million copies.
The most important thing about the three puzzles above is that you can work them out right now, if you have initiative and patience (and a little knowledge of physics). No mathematical training is required. There are some hints at the bottom of the page, and below that, the answers.
Gardner specialised in such puzzles, having studied closely the works of the masters of an earlier generation, England’s Henry Dudeney and his American counterpart, Sam Loyd.
The reward for solving puzzles like these, unaided, is to experience priceless Aha! moments. “Googling it is not the Gardner way,” says the philosopher Bob Crease in Physics Today this month. “The Gardner way is to ignite your fascination so that you experience the pleasure of finding the answer yourself.”