A system uses 3 page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? 4, 7, 6, 1, 7, 6, 1, 2, 7, 2

We trace the LRU replacement algorithm with 3 page frames initialized to empty:

1. Reference 4: Page fault $\rightarrow$ Frames: [4] (Fault 1)

2. Reference 7: Page fault $\rightarrow$ Frames: [4, 7] (Fault 2)

3. Reference 6: Page fault $\rightarrow$ Frames: [4, 7, 6] (Fault 3)

4. Reference 1: Page fault. The least recently used page is 4. Replace 4 with 1 $\rightarrow$ Frames: [1, 7, 6] (Fault 4)

5. Reference 7: Hit $\rightarrow$ Recency order (MRU to LRU): 7, 1, 6

6. Reference 6: Hit $\rightarrow$ Recency order (MRU to LRU): 6, 7, 1

7. Reference 1: Hit $\rightarrow$ Recency order (MRU to LRU): 1, 6, 7

8. Reference 2: Page fault. The least recently used page is 7. Replace 7 with 2 $\rightarrow$ Frames: [1, 6, 2] (Fault 5). Recency order: 2, 1, 6

9. Reference 7: Page fault. The least recently used page is 6. Replace 6 with 7 $\rightarrow$ Frames: [1, 2, 7] (Fault 6). Recency order: 7, 2, 1

10. Reference 2: Hit $\rightarrow$ Recency order: 2, 7, 1

Total number of page faults = 6.