September 2011
Problem of the Month

How Many Games?

If all of the following statements about the number of games in Mr. P's collection are true, what is the number?

1. The number has three or four digits.

2. The number is palindromic (its digits are the same written forward and backwards).

3. The number is prime.

4. If Mr. P had 40 more games, statements 1 through 3 would all still be true.

Solution to the Problem:

The number is 313.

All four-digit palindromic numbers are divisible by 11 and therefore are not prime, so these can be ruled out.
There are only 15 three-digit palindromic primes ranging from 101 to 929, and I thought only two of them (313 and 353) had a difference of 40.

However, James Alarie and John Funk sent in three answers that work:
151 + 40 = 191
313 + 40 = 353
757 + 40 = 797.
And then Serdar Yuksekkaya and Denise Peterson each sent in two correct solutions.
So, James, John, Denise, and Serdar get extra credit for this month!!

Correctly solved by:

1. James Alarie	Flint, Michigan
2. John C. Funk	Ventura, California
3. Serdar Yuksekkaya	----------
4. Denise Peterson	Sikeston, Missouri

Send any comments or questions to: David Pleacher