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Paying daily wages from a seven-segment gold bar

Question

A gold bar is made of seven equal segments. A worker must be paid exactly one segment per day for seven days, and you may take back pieces as change. Where should you make just two breaks?

Short answer

Break off pieces of 1, 2 and 4 segments. That means cutting after the first segment and after the third. Every total from 11 to 77 is a sum of distinct powers of two, so each day you can hand over and swap back pieces to make the worker's cumulative pay correct.

Adapted from Crack, Heard on the Street, Q1.56, p.19; question and answer rewritten by SelfMadeQuant.com.

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