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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 plan (spoiler) | Comment 2 of 4 |
Jer has done all the hard work.  The plan itself is not daunting at all.

Each tire can spend 6090 miles in each position (left front, right front, left rear, right rear, spare in trunk).  Every 6090 miles, move each tire clockwise (ie, left front to right front, right front to right rear, right rear to trunk, trunk to left rear, left rear to left front).

Of course, the left front and right front get identical wear, so a slightly more complicated scheme will involve fewer moves, but this one works well enough and is easy to remember.

 Posted by Steve Herman on 2013-08-20 11:50:17

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