If you have 8 marbles and one is lighter than the rest, how would you determine which one is lighter using a balance scale in two weighings?

Free worked solution · Quant Blueprint

Weigh three against three; then use one comparison within the remaining candidate group.

1. Label the marbles A through H. Weigh ABC against DEF.
2. If ABC is lighter, the candidate is A, B or C; if DEF is lighter, it is D, E or F. Weigh any two candidates: the lighter one is defective, or the unweighed third is defective if they balance.
3. If the first weighing balances, the candidate is G or H. Weigh G against H and take the lighter one.
4. Two weighings suffice in every branch. One cannot suffice because a balance has at most three outcomes but there are eight possible defective marbles.

Common mistake

Do not begin with four against four: that leaves four candidates in a light group, which one final three-outcome weighing cannot always resolve.

Follow-up

For a known lighter marble, two weighings can distinguish up to nine candidates using a 3-vs-3 first weighing. If the defect could be heavier or lighter, the state space changes.

Original educational explanation for this practice question. Reviewed 2026-10-13. Firm-style practice; the label describes the collection’s preparation context.