THE ANSWER IS 9 TIRES. If you rotate 9 tires you can avoid buying 12 tires.
Miles
| tire 1 | 300 | 300 | 300 | 300 | |||||
| tire 2 | 300 | 300 | 300 | 300 | |||||
| tire 3 | 300 | 300 | 300 | 300 | |||||
| tire 3 | 300 | 300 | 300 | 300 | |||||
| tire 4 | 300 | 300 | 300 | 300 | |||||
| tire 5 | 300 | 300 | 300 | 300 | |||||
| tire 6 | 300 | 300 | 300 | 300 | |||||
| tire 7 | 300 | 300 | 300 | 300 | |||||
| tire 8 | 300 | 300 | 300 | 300 |