Solution

The Mislabeled Jars

Show the problem again

Three jars contain apples, oranges, and a mix of both, respectively, but all three labels are wrong. Without looking inside, you may draw fruit one piece at a time from any jar. What is the minimum number of draws that guarantees you can correctly relabel all three jars?

Worked solution

The answer is 1: draw from the jar labeled "Mixed." Since every label is wrong, that jar is pure, and the drawn fruit reveals which. Say you draw an apple: that jar is Apples. The jar labeled "Oranges" cannot be Oranges (wrong label) and cannot be Apples (taken), so it is Mixed, leaving the "Apples" jar as Oranges. One draw fully determines the configuration.

Source: Classic mislabelled-jars deduction puzzle in wide circulation; no traceable original source. Statement written for AxiomIQ.