Name the three sacks A, B, and C, and their correct contents a, b, and c. Suppose you open A. Since all labels were misplaced, there are only two possibilities: 1) you see b, or 2) you see c. Without loss of generality, suppose A contains b.
This means that B must contain c. Otherwise we end up violating the rule -- if B contains a, then C would be left with c, violating the assumption that all labels have been misplaced. If B contains b, this again violates the same assumption.
Thus, we are left with a for C.One investigation is sufficient to reveal the contents of the sacks.
Answer: one.
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