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The Palindromic Odometer

The Puzzler


RAY: This came in from Terry Sare and I didn't even have to change it.

Terry writes, "I was driving on the highway the other day recently and I happened to notice my odometer. Like most odometers nowadays, it shows six digits, in whole miles only -- no tenths of a mile. So, if my car had 300,000 miles, for example, I'd see 3-0-0-0-0-0. And that's all. Until I drove another mile, at which point it would read 3-0-0-0-0-1.

"Now, what I saw that day was very interesting. I noticed that the last 4 digits were palindromic, that is they read the same forwards as backwards. For example, "5-4-4-5" is a palindrome. So, my odometer could have read 3-1-5-4-4-5, with those last four digits, starting with the units, then the tens, then the hundreds, and finally the thousands, being the palindrome.

"One mile later, the last 5 numbers were palindromic. For example, it could have read 3-6-5-4-5-6.

"One mile after that, the middle 4 out of 6 numbers were palindromic. So, the first and last numbers weren't involved in the palindrome, but the middle 4 were palindromic.

"And you ready for this? One mile later, all 6 were palindromic! For example, 2-1-3-3-1-2. "

Pretty good, huh? I thought so. So, here again are the conditions as stated by Terry. "I noticed that the last 4 digits were palindromic. I drove a mile, and the last 5 were palindromic. I drove another mile and the middle 4 were palindromic, and the ends were not involved. And then one mile later, all 6 digits were palindromic."

The question is, what did Terry see on the odometer when he first looked?

Think you know? Drop Ray a note!

[ Car Talk Puzzler ]

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