perplexus.info :: Numbers : Mileage

Mileage (Posted on 2004-06-16)

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.

Submitted by Brian Smith

Rating: 3.0000 (1 votes)

Solution: (Hide)

Part 1: 786 miles
12345 + 786 = 13131; 123 + 786 = 909
Part 2: 124 miles
12345 - 124 = 12221; 123 - 124 = 999 (mod 1000)
Part 3: Travel until the trip meter is a palindrome. The mileage meter will look like 'abcde'. Then travel a multiple of 1000 miles to make the mileage meter read 'edcde'.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer to Part 2	K Sengupta	2023-12-23 01:24:48
Puzzle Thoughts	K Sengupta	2023-03-05 06:57:49
Puzzle thoughts to part 1	K Sengupta	2022-12-30 04:40:18
generalization	Charlie	2004-06-16 10:08:07
re: Code used for finding palindromic numbers - no spoiler	Charlie	2004-06-16 10:03:20
Code used for finding palindromic numbers - no spoiler	Erik O.	2004-06-16 09:48:43
Solution to part 1 - plus hints for the proof.	Erik O.	2004-06-16 09:42:31
Part 2 solution (last time)	Jenny Turner	2004-06-16 08:49:35

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