A car has four wheels, so in 27,000 miles the car goes through 108,000 tire-miles. If each tire lasts 12,000 miles, they’ll need 9 tires.

But the question remains how to use them. After the first 12,000 miles they’ll discard the first four tires together, leaving five tires to get them through the remaining 15,000 miles. The answer is to change one tire every 3,000 miles, so that the car runs on these tires:

First 3000 miles: Tires 1, 2, 3, 4
Second 3000 miles: Tires 2, 3, 4, 5
Third 3000 miles: Tires 3, 4, 5, 1
Fourth 3000 miles: Tires 4, 5, 1, 2
Fifth 3000 miles: Tires 5, 1, 2, 3

In this way each tire will be used no more than 12,000 miles.