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Sending a locked box through a thieving courier

Question

You need to get a document to a friend using a courier who will steal anything not secured by a lock. You and your friend each own a padlock and its only key, and neither of you has a key to the other's lock. A box can take several padlocks. How do you get the document delivered safely?

Short answer

Use a double-lock round trip. Put the document in the box, lock it with your padlock and send it; your friend adds their own padlock and sends it back; you remove yours and send it again; your friend unlocks their padlock. The box is never in transit unlocked, and no key ever has to travel.

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 2.3 Thinking Out of the Box, 'Message delivery', p.12; question and answer rewritten by SelfMadeQuant.com.

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