Car Talk Puzzler (Palindrome Mileage)

New Math Puzzler up this week:

Tommy’s Drive to Work
RAY: Tommy has a new car, it’s 19 years old. … It has one of those newfangled six-digit odometers. It can register as many as 999,999 miles. 
So one fine morning last week, Tommy gets into his new car to drive to work. He fires up his engine and before pulling out of the driveway, he notices something interesting. His odometer reading is a palindrome. Do you know what a palindrome is?

TOM: No.

RAY: It’s a number that reads the same forwards as it does backwards. For example, if his odometer read 175,571 miles, that’s a palindrome number. 1 – 7 – 5, 5 – 7 -1, reads the same forward and backwards. ‘Well, that’s cool,’ he says to himself, and off he goes.

Naturally, he’s in no hurry to get to work, so he stops at his favorite café and gets his usual quadruple espresso macchiato, and about an hour later, he shows up at Car Talk Plaza. Just as he pulls into his ‘Reserved for the Big Cheese’ parking spot, he notices that his odometer reading again is a palindrome. And no, the odometer is not broken, but it is indeed a palindrome number once again.

So he’s gotten in the morning, seen a number, driven some number of miles – not many, cause he only drove for an hour,–not even, most of the time he was drinking coffee — and his new odometer reading is again a palindromic number.

Here’s the question: How far did he drive that morning?

I have a couple of answers with the same amount of miles, but it seems too low for driving for an hour. Even in a city.

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4 Responses to Car Talk Puzzler (Palindrome Mileage)

  1. krislikesmath says:

    Hmmm, I didn’t hear that hour part. I thought he said something like “within the hour,” or “again that morning” and didn’t use a hard hour as a guide. I found 110 mile palindromes and 11 mile palindromes and it would seem that one is far too and one is too short. However in traffic I could easily make only 11 miles an hour, but it all depends.

    Check out my analysis:

    • Dan says:

      Yea, 11 miles seems too low, and 110 seems way too high. We’ll see!

      Nice blog btw, beer and visualizations of data. Added it to my google reader.

  2. Sally says:

    Remember, he stopped at a cafe for his favorite “macchiato”, so he wasn’t driving for the full hour.

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