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Suppose you know that tires on the rear of your car will wear out after 21000 miles, while tires on the front of your car last for 29000 miles. Suppose you have a new car and five identical new tires (four installed and one spare.) What is the maximum distance you can drive, assuming you can easily change the tires any time you want?

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 2.5000 (2 votes)

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 A lazy plan | Comment 3 of 4 |
I don't know why I bother, since I can easily change tires, but here is a rotation scheme that involves only rotating 3 tires every 6090 miles.  Every 6090 miles, move one of the front tires to the rear, one of the rear tires to the trunk, and the spare to the front.  But be sure to keep track of which tire is which!

Positions in each rotation
Tire 1  F  F  R  R  S
Tire 2  F  R  R  S  F
Tire 3  R  R  S  F  F
Tire 4  R  S  F  F  R
Tire 5  S  F  F  R  R

The only problem with this scheme (and the previous one) is that my spare is completely bald for the last 6090 miles.  If this is a concern, rotate more frequently.

 Posted by Steve Herman on 2013-08-20 12:05:45

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