Overview
This puzzle turns a guarantee — that every label is wrong — into information. A wrong label doesn't just fail to help; it actively tells you what a box is not.
How to solve The Mislabeled Boxes
- Draw from the box labelled 'Mixed'. Its label is wrong, so it isn't mixed — it's pure one fruit.
- The fruit you draw reveals that box's true contents (say, apples).
- The other two boxes are then forced: each can't be what its wrong label says, and one identity is already used.
The key insight
Only the 'Mixed' box guarantees a decisive draw — a pure box gives an unambiguous answer, whereas drawing from a truly mixed box could mislead. The all-labels-wrong condition then cascades the rest.
Variations & echoes
- If only some labels were wrong, one draw would no longer be enough.
- It's a neat example of using a global constraint to collapse a search.
Frequently asked questions
Why not draw from the 'Apples' box?
That box could be Oranges or Mixed, so a single draw might not distinguish them. The 'Mixed' box is guaranteed pure, giving a clean answer.