# Scientific American screws up Martin Gardner’s last article

Scientific American has republished on its web site Martin Gardner’s last article for the magazine. It’s from 1998, well after Gardner stopped his long-running “Mathematical Games” column. Unfortunately, SA screwed up the article’s HTML, making part of it incomprehensible.

Here’s the section that’s messed up:

Let me propose to teachers the followingexperiment. Ask each group of students to think of any three-digit number—let’s call it ABC. Then ask the studens to enter the sequence of digitstwice into their calculators, forming the number ABCABC. For example, if the students thought of the number 237,they’d punch in the number 237,237. Tell the students that you have the psychic power to predict that if they divide ABCABC by 13 there will be no remainder. This will prove to be true. Now ask them to divide the result by 11. Again, there will be no remainder. Finally, ask them to divide by 7. Lo and behold, the original number ABC is now in the calculator’s readout. The secret to the trick is simple: ABCABC = ABC ≤ 1,001 = ABC ≤ 7 ≤ 11 ≤ 13. (Like every other integer, 1,001 can be factored into a unique set of prime numbers.) I know of no better introduction to number theory and the properties of primes than asking students to explain why this trick always works.

A cute little puzzle. Too bad the formula

ABCABC = ABC ≤ 1,001 = ABC ≤ 7 ≤ 11 ≤ 13

makes no sense at all. A little thinking reveals that what they really meant—and what was surely in Gardner’s original—was

ABCABC = ABC × 1,001 = ABC × 7 × 11 × 13

At first I thought the symbol mixup was an encoding problem. It’s not uncommon for web pages to be written in one encoding and viewed in another, especially if the author doesn’t specify the encoding in the <head>. That can lead to goofy symbols. But looking at the source HTML of the page, I saw that the problem was much simpler: whoever HTMLified the article just screwed up the entities. The source of the offending equation is

ABCABC = ABC &le; 1,001 = ABC &le; 7 &le; 11 &le; 13


ABCABC = ABC &times; 1,001 = ABC &times; 7 &times; 11 &times; 13

I’m not sure what kind of “web professional” thinks &le; is going to generate a multiplication sign, nor do I understand how an editor could let that slip through. Even worse, one of the commenters on the article pointed out the mistake (at least he tried—the SA comment system garbled the symbols in his explanation), and it’s still there.