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Number TheoryHardDigits and Bases

Digits and Bases · Hard problem

A balance has one weight each of 1,3,9,271, 3, 9, 27 and 8181 grams, and weights may go on either pan. A 5050-gram object sits on the left pan. What is the total mass, in grams, of the weights that must go on the LEFT pan (with the object) to balance it?