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Mileage (Posted on 2004-06-16) Difficulty: 3 of 5
My car has a 5-digit odometer, which measures the miles since the car was built, and a 3-digit trip meter, which measures the miles since I last set it. Every so often, one or both of the readings is a palindrome. The meters reset to 000 after 999 and to 00000 after 99999.

The current readings are 123 and 12345. Assuming that I do not reset the trip meter, when is the next time both readings will be palindromes?

When was the most recent time both readings were palindromes?

Prove no matter what the mileage and trip meters read, they can eventually be made to both be palindromes without resetting the trip meter.

Note: A palindrome reads the same forwards and backwards, like 262 or 37173.

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutiongeneralizationCharlie2004-06-16 10:08:07
re: Code used for finding palindromic numbers - no spoilerCharlie2004-06-16 10:03:20
Some ThoughtsCode used for finding palindromic numbers - no spoilerErik O.2004-06-16 09:48:43
SolutionSolution to part 1 - plus hints for the proof.Erik O.2004-06-16 09:42:31
Part 2 solution (last time)Jenny Turner2004-06-16 08:49:35
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