## Palindromic Distance

#### Problem

Julie is a careful driver and never breaks the speed limit. One day as she set off on a journey in her car she noticed that the odometer was displaying 13931 miles, which was palindromic (the same forwards and backwards). After completing the journey, which took two hours, Julie could not believe that it was palindromic once more.

What was her average speed during the journey?

#### Solution

The next palindrome after 13931 is 14041. Completing 14041 13931 = 110 miles in two hours is an average speed of 55 mph. If we considered the next palindromic example, 14141 13931 = 210, which means she drove at 105 mph, but we were told that she never breaks the speed limit.

Problem ID: 267 (11 Feb 2006) Difficulty: 1 Star