312.Paying With a Gold Bar
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A worker will work 15 days and must hold exactly x/15 of a gold bar at the end of day x, for every x from 1 to 15. You may take pieces back as well as give them. What is the minimum number of cuts needed to divide the bar so this is always possible?
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Think in binary. Which piece sizes let you represent every total from 1 to 15 while handing back what you overpaid?
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