Mathematical challenges have captivated the most brilliant minds of history. More recently, they have captured the public interest, thanks largely to the work of Martin Gardner, who popularized math and logic problems like these:
1. Can you draw four straight lines that pass through the nine points of the picture, without lifting the tip of the pen from the paper?
2. How quickly you can multiply these numbers?
256 x 3 x 45 x 3961 x 77 x 488 x 2809 x 0
3. Can you choose six digits from the illustration that add up to 21?
We will leave the solutions for the end. These puzzles can be solved soon after seeing them on the screen —if one is able to think differently— or give up after turning them over in one’s head. What purpose do mathematical problems serve? For Martin Gardner (1914-2010) they were a way to get people interested in mathematics. As he used to say in the magazine Scientific American, where he spent over twenty years publishing a monthly column on mathematical games, «Surely the best way to wake up a student is to present him with an intriguing mathematical game, puzzle, magic trick, joke, paradox, model, limerick, or any of a score of things that dull teachers tend to avoid because they seem frivolous.»
However, Gardner was more than a disseminator of mathematical games. This scholar of philosophy devoted much of his life to journalism and to the popularization of science in general. But of all the things he did, that which made him famous worldwide was his legendary monthly mathematical games section, collected in books like Aha! Gotcha: Paradoxes to Puzzle & Delight or Knotted Donuts and Other Mathematical Entertainments.
In addition, Gardner was a tireless skeptic. Together with his friends Isaac Asimov and Carl Sagan, he founded in 1976 the Committee for Skeptical Inquiry (CSI, formerly known as CSICOP), an organization dedicated to the reporting of pseudoscience, to which he turned once he had abandoned his column on recreational mathematics. “Scientists and science writers have a duty to expose the errors of false science, especially in the field of medicine,” he said. Some examples of his writings on pseudoscience include the books Science: Good, Bad and Bogus (1981), New Age: Notes of a Fringe Watcher (1988), On the Wild Side (1992) and Did Adam and Eve Have Navels? (2000).
But, without doubt, his true bestseller was The Annotated Alice (1960). In it, we discover the mathematical concepts, encoded messages and chess games hidden in the work of Lewis Carroll.
Gardner, as recounted in his book Mathematics for fun (1988), hoped that readers could “resist the temptation to look up the answer before they sincerely tried to solve the problem.” And whether they found the right answer or not, he wished that “they were happy for having been confused.”
And now, as promised, here are the solutions:
2. Did you notice the zero at the end before starting to multiply? If you see it, you’ll know immediately that the final answer must be zero.
3. Rotate the picture and choose 3 sixes and 3 ones.