December 31, 2001
Problem of the Month

The Palindromic Year Problem

The Year 2002 is a palindromic year (it reads the same backwards as forwards).

The last one occurred in 1991, so we have lived to see two palindromic years.

However, most people only live to see one Palindromic year since recently, they have occurred 110 years apart (1991, 1881, 1771, 1661, ...).

Starting with the Year 1 AD, what period of 100 years contains the most number of palindromic years?

Solution to the Problem:

There are two answers:
The years 1 to 100 AD and the years 2 to 101 AD both contain 18 palindromic years.

Scanning back through the years, in the four-digit years: most palindromic years are separated by 110 years;

in the three-digit years: most are separated by 10 years (999, 989, 979, ...), so in a span of 100 years (from 900 to 999) there are ten palindromic years;

But the most Palindromic years occur in the single- and two-digit years: 101, 99, 88, 77, 66, 55, 44, 33, 22, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1.

Correctly solved by:

1. Richard K. Johnson	La Jolla, California
2. Keith Mealy	Cincinnati, Ohio
3. Rick Jones	Kennett Square, Pennsylvania
4. Walt Arrison	Philadelphia, Pennsylvania
5. Jaime Garcia	Winchester, Virginia
6. John Beasley	Winchester, Virginia
7. Jacob Baker	Winchester, Virginia
8. Laurence O'Neill	Winchester, Virginia
9. Bob Hearn	Winchester, Virginia
10. David & Judy Dixon	Bennettsville, South Carolina
11. David Powell	Winchester, Virginia
12. Travis Riggs	Winchester, Virginia
13. Joe Jenkins	Winchester, Virginia
14. George Gaither	Winchester, Virginia
15. Jaime Lockhart	Winchester, Virginia
16. Matt Crandell	Winchester, Virginia
17. James Alarie	University of Michigan -- Flint
18. Nick von Keller	Winchester, Virginia
19. Brandon Copple	Winchester, Virginia
20. Tori Eads	Winchester, Virginia

Send any comments or questions to: David Pleacher