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It's a Puzzlement

Palindrome Challenge

by John P. Robertson

"Ana, nab a banana" is a palindrome, which means it reads the same backwards and forwards, ignoring spacing and punctuation. More familiar ones are "Madam, I'm Adam," "A man, a plan, a canal: Panama!" and "Able was I ere I saw Elba." This last is easily corrupted into "Amiable was I ere I saw Elba, Ima." Sadly, because he was speaking to Eve and not to Ada, the reply to the first was not, "Adam, I'm Ada." Lovers of palindromes were saddened when the shop in California, named the Yreka Bakery, went out of business.

In honor of the fact that 2002 is a palindromic year, we offer a creative challenge: create a palindrome that touches on actuarial science, insurance, or other areas related to actuarial work. These can be phrases, sentences, or poems. While "letter-by-letter" palindromes, such as those above, are what we are mostly looking for, "word-by-word" palindromes, such as, "So patient a doctor to doctor a patient so" will also be considered. There are several Web sites that list palindromes. A book with a good chapter on palindromes is The Oxford Guide to Word Games by Tony Augarde.

We will print the best entries in the February 2003 issue (two issues hence), and post all the entries on the CAS Web Site. Mark Saltveit, editor of the Palindromist magazine, has graciously offered to help judge entries for originality, difficulty, and wit. Due to the need to review submissions, we need to receive them by October 10, 2002. Prizes of CAS coffee mugs, or the like, will be awarded to the three entries that are the best, in the opinion of the reviewers.

Submit your entries by e-mail to or to, or mail or fax them to the CAS Office. It's fine to submit more than one entry, but only the first 99 entries from any one individual will be read. If submitting by e-mail include your name in the body of the e-mail, and in the body of any attachment (MS Word or PDF file preferred, but try us). Sometimes we cannot deduce your name from the e-mail address, or that address is missing by the time the e-mail arrives.

A Pile of Pennies

You were given a pile of more than 10 pennies and you were told that exactly 10 of them were face up. You were asked to make two piles with the same number of heads, under conditions that did not let you see the pennies, or feel them well enough to determine their orientation. You could manipulate and turn over individual pennies.

Bob Gardner was one of a number of solvers who suggested making one pile of 10 pennies and one pile of the remaining pennies. You then turn over each penny in the pile of 10. Now the number of heads in each pile is the same, namely 10-k, where k was the number of heads in the pile of 10 before they were inverted.

But this is the CAS, so there were other creative solutions. David Uhland suggested balancing them all on edge, to make two groups that each had no heads. Brian D. Haney notes that if you scrape one penny across the columns of the Lincoln Memorial on a second penny, a distinctive "washboard" sound is made. This can be used to determine which side is tails, and then it is easy to finish the puzzle. Stuart Klugman sent a deliberately silly parody of a CAS exam answer, that is, he read the puzzle very literally. He notes that we didn't specify how many piles one was to make, nor did we specify that you had to say which two piles had the same number of heads. So he separated the n pennies into n piles of one penny each, and observes that some two piles have one head each, and so the same number.

Nathan J. Babcock, Don Behan, Roger Bovard, Lee M. Bowron, Peter Burchett, Jonathan Evans, Steve Fallon, Barry Franklin, Dan Goddard, Robert Giambo, Marshall Grossack, John C. Hanna Jr., John Herder, Paul Ivanovskis, Alex Kozmin, Dave Oakden, Tim Polis, Marn Rivelle, Daniel Roth, Gary Venter, Christopher Yaure, and Mike Ziniti also submitted solutions.