Answer:

1.  1. The initial value of the counters is: 0


2. Counters are add 1 when each page frame replace a new page.(new page是指之前没有出现过的页面)


3. Counters are minus 1 when the replaced page was not appeared.（也就是在之后的页面中都不再出现）


4. Every time a new page need to replace page frame, first to determine all the page frames, select the current counter value is the smallest frame as a replacement pages, if there are multiple page frames of the same counter value, then select the page which first enter page frame as the replacement page.


5. reference string: 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2

c represent counter

M represent Miss, also page fault

H represent Hit

Page frame1	1(M, c=1)	1(c=1)	1(c=1)	1(c=1)	5(M, c=2)	5(c=2)	5(c=2)	5(c=1)	5(c=1)	5(c=1)
Page frame2		2(M, c=1)	2(c=1)	2(c=1)	2(c=1)	2(c=1)	2(c=1)	2(c=1)	2(c=1)	2(c=1)
Page frame3			3(M, c=1)	3(c=1)	3(c=1)	3(H, c=0)	3(c=0)	1(M, c=0)	6(M, c=0)	7(M, c=1)
Page frame4				4(M, c=1)	4(c=1)	4(c=1)	4(H, c=1)	4(c=1)	4(c=1)	4(c=1)
Page frame1	5(c=1)	5(c=1)	5(c=1)	5(c=1)	5(c=1)	5(c=1)	5(c=1)	5(H, c=1)	5(c=1)	5(H, c=0)
Page frame2	8(c=2)	8(c=2)	8(H, c=2)	8(c=2)	8(c=2)	8(H, c=1)	8(c=1)	8(c=1)	8(c=1)	8(c=1)
Page frame3	7(M, c=1)	7(H, c=1)	7(c=1)	7(c=1)	7(H, c=0)	7(c=0)	7(c=0)	7(c=0)	4(M, c=0)	4(c=0)
Page frame4	4(c=1)	4(c=1)	4(c=1)	9(M, c=2)	9(c=2)	9(c=2)	9(H, c=1)	9(c=1)	9(c=1)	9(c=1)
Page frame1	5(c=0)	2(M, c=0)
Page frame2	8(c=1)	8(c=1)
Page frame3	4(H, c=0)	4(c=0)
Page frame4	9(c=1)	9(c=1)

So there are 12 page faults

Page frame1	1(M)	1	1	1	1	1	1	1(H)	6(M)	6
Page frame2		2(M)	2	2	5(M)	5	5	5	5	5
Page frame3			3(M)	3	3	3(H)	3	3	3	7(M)
Page frame4				4(M)	4	4	4(H)	4	4	4
Page frame1	8(M)	8	8(H)	8	8	8(H)	8	8	4(M)	4
Page frame2	5	5	5	5	5	5	5	5(H)	5	5(H)
Page frame3	7	7(H)	7	7	7(H)	7	7	7	7	7
Page frame4	4	4	4	9(M)	9	9	9(H)	9	9	9
Page frame1	4(H)	4
Page frame2	5	2(M)
Page frame3	7	7
Page frame4	9	9

So there are 11 page faults.