Payment in Gold

Logic Level 3

Arun has a gold bar of mass 63 grams. He hired a daily worker, and promised to pay 1 gram of gold for each day of work. The worker will be working for 63 days, which means he will end up with the entire gold bar at the end. However, Arun cannot simply pay the worker at the end of the time period, but has to adhere to union laws.

Local union laws require that the worker must be paid daily, meaning that after \(X\) days of working, the worker must posses \(X\) grams of gold. What is the minimum number of pieces that Arun has to divide the gold bar into, to ensure that he can pay the daily working in accordance with union laws?

Note: Arun has full control over the size of the pieces, and may be divide the gold bar in any manner. For example, he can divide the gold bar into pieces of \( 5, 6\) and 52.

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