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This problem trains for: AMC-8, AMC-10, AMC-12.

What is the largest base-10 number that can be written in base 60 as a three digit number?

Assume S is the largest value of a digit in base 60. Then, in base 10:

equation

and the largest three digit number in base 60 is:

equation

Writing this number in expanded form we obtain its value in base 10:

equation

equation

equation