G'day guys

I've spent many hours with pencil and paper, I certain, but am asking in case 
someone older-n-wiser can offer sage words:

If I want to backup a system for n days, and be able to recover any particular 
days files the only way that I can see is to have a daily backup for n days.

Tower of Hanoi (for eg) says you can backup 2^^n-1 days with n tapes but i can 
break that. Simple EG starting with day 4 sequence ie backup:

C A B A C A B A  (http://en.wikipedia.org/wiki/Backup_rotation_scheme)

On day 2 you create a file, which you remove on day 3. On day 6 you try to 
restore day 2 ....

On day 6 you have:
A from day 5
B from day 2 (or worse from day 6)
C from day 4

So the file created on day 2 backed up on day 3 is lost.
Can anybody point to the boat (I've missed) or confirm my vision.

Thanks
James 
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