Two Cuts, Seven Paydays

A shipwright agrees to restore a yacht over seven days, her fee being a slim platinum bar. She insists on holding exactly k/7 k/7 of the bar at the end of day k k — no more, no less — for every one of the seven days. You may cut the bar in only two places, and pieces may be traded back and forth at each evening settlement. Where do you cut, and what changes hands each evening?

Answer

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