Three Mislabelled Jars Puzzle

Problem Three jars: one all oranges, one all apples, one a mix. ALL THREE labels are wrong. What is the minimum number of fruit draws to relabel every jar correctly?

Input / Output

• A reasoning puzzle: state the answer and prove both sufficiency and necessity.

Example

• Answer: 1 draw.

Expected approach

• Draw from the jar labelled "mix". Since every label is wrong, that jar is pure — the drawn fruit names it (say, orange). The jar labelled "apples" can't hold apples (wrong label) and can't be the oranges jar (taken), so it's the mix; the remaining jar is apples. Sufficiency shown; necessity: zero draws leaves multiple consistent assignments, so 1 is minimal. The evaluated skill is exploiting the "all labels wrong" constraint and arguing the lower bound, not just recalling "1".