Discussion

The *-marked references cause page replacements.

Which one or more of the following could be the page replacement policy/policies in use?

Answer: D

The policy could only be the Optimal page replacement policy.

Check each replacement against the policies, counting for LFU and MFU every reference made to a page so far:

Reference 4 (frames 1, 2, 3): page 2 is replaced. Optimal evicts the page used farthest in the future: 1 is next used at the 7th reference, 3 at the 12th, 2 at the 13th, so 2 goes. LRU would evict 1, the least recently used, so LRU is ruled out.
Reference 6 (frames 1, 4, 5): page 1 is replaced. Optimal agrees (next uses: 4 at the 9th, 5 at the 10th, 1 at the 11th). LFU would evict 5, referenced once, against twice for 1 and 4, so LFU is ruled out.
Reference 3, the 12th (frames 6, 1, 5): page 5 is replaced. Page 1 has by then been referenced three times, 5 twice and 6 once, so MFU would evict 1, ruling MFU out. Optimal is free to evict 5, since none of the three pages is used again.

The remaining replacements (5 replaces 3, 1 replaces 4, 2 replaces 6) also agree with Optimal, so it is consistent with every step.

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