MathTrek

In this country a date such as July 4, 1971, is often written 7/4/71, but in other countries the month is given second and the same date is written 4/7/71. If you do not know which system is being used, how many dates in a year are ambiguous in this two-slash notation?

This brainteaser leads off a collection of 340 entertaining and thought-provoking puzzles and problems posed by Martin Gardner in his famous "Mathematical Games" columns for Scientific American. The puzzles appear in a thick volume, The Colossal Book of Short Puzzles and Problems, recently published by W.W. Norton.

Computer scientist Dana Richards of George Mason University combed through Gardner's columns to select the puzzles for the collection and sorted the material into four broad areas: combinatorial and numerical problems, geometric puzzles, algorithmic puzzles and games, and miscellaneous pastimes (including logic, word play, and physics puzzles). The puzzles in each category are also arranged, roughly, from easiest to hardest. Twelve of the puzzles are new, selected from the hundreds that Gardner, now in his 90s, has gathered since he left Scientific American in 1986.

This book serves as a companion to an earlier volume, The Colossal Book of Mathematics, also published by Norton, which features 50 of Gardner's most popular columns.

Of course, if you want the complete set of Gardner's Scientific American articles, you can turn to the CD-ROM recently published by the Mathematical Association of America. The collection is not only complete but also readily searchable!

I have long been a great fan of Martin Gardner's writings. I obtained my first issue of Scientific American in 1962, when I was in the ninth grade. The magazine happened to feature a series of articles on Antarctica, which was the topic of study in my geography class. But it was Gardner's discussion of tests that show whether a large number can be divided by a number from 2 to 12 that really caught my attention. From that time on, I never missed his articles.

Gardner's last Scientific American column appeared in May 1986. Two decades later, his articles continue to amaze and delight.

Answer: Each month has 11 ambiguous dates (a date such as 8/8/71 is not ambiguous), making 132 in all.

Here's one of the new puzzles.

A 20-page newspaper consists of five double sheets. One of these sheets is selected at random. Its four page numbers are added. Can you name the sum?

References:

Gardner, M. 2006. The Colossal Book of Short Puzzles and Problems, D. Richards, ed. New York: W.W. Norton.

______. 2005. Martin Gardner's Mathematical Games: The Entire Collection of His Scientific American Columns. Washington, D.C.: Mathematical Association of America.

______. 2001. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. New York: W.W. Norton.

Peterson, I. 1997. Martin Gardner's lucky number. Science News Online (Sept. 6). Available at http://www.sciencenews.org/pages/sn_arc97/9_6_97/mathland.htm.