America is famously pluralistic, but this is ridiculous. We received nearly 300 responses to Horizon's "connect the dots" puzzle published Oct. 13 -- and almost that many different answers! Is this a great country, or what?
The puzzle asked: "How many squares of different sizes can you make by connecting four of the dots" in a 5-by-5 matrix. Among the most popular reader answers were 1, 3, 4, 7, 8, 22, 24, 25, 30, 33, 35, 40, 45, 50 and 55, to cite a few.
The answer we had in mind was eight, as per the Cool Math Dudes web site at http://library.advanced.org/2883/ [see diagram], one of many neat things brought to you by ThinkQuest.
It's a terrific Internet-based education program that hosts a host of web sites created by teachers and students. Check 'em out at http://www.thinkquest.org.
However, different numbers turn out to be correct, thanks to two particularly imbecilic mistakes in the way our editor -- who claims to be a native English speaker -- phrased the question:
(1) "Squares of different sizes" is imprecise. Most folks would construe that to mean "how many squares, each of a different size, can be made" But it is technically possible to interpret it as "how many squares of any size at all" can be made.
(2) Worse yet, a few readers revealed an even dumber error. Mathematician Dale Hodges of Fall Church sums it up:
"The proper answer is that there are an infinite number of squares. By your exact wording of the question, you say to draw any square that connects four dots. It does not specify that the four dots must be the four corners.
"Take the first four dots to the top row (or any four dots in a row anywhere), and from those four dots you could draw a straight line of any length which would generate a square (actually any infinite number of squares if you don't have to stay in the plane of the dots). Therefore, there are an infinite number of different squares."
Hoo, boy. In a veritable orgy of contrition, we're sending T-shirts to the first 50 folks who sent in either our preferred answer or any answer consistent with the mile-wide ambiguities noted above.
Meanwhile, the saga continues. This month's contest is based on an apparently facetious question -- "Why do we drive on a parkway and park on a driveway?" It was submitted by Frank Bryan of Fort Washington.
We have no answer for this. But we do have a lot of the hugely esteemed Horizon T-shirts and will award one to the 25 folks who send us the best examples of similarly illogical instances of English usage.
We'll also print the best dozen or so in the Dec. 8 issue, along with the submitters' names.
Send your entries to email@example.com or Horizon, The Washington Post, 1150 15th St. NW, Washington, D.C. 20071. We absolutely cannot accept entries by phone.