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2012 Spring CHMMC Tiebreaker 4 - numbers 1-6 in fractions, min result

Source:

March 1, 2024
algebraCHMMC

Problem Statement

The expression below has six empty boxes. Each box is to be fi lled in with a number from 11 to 66, where all six numbers are used exactly once, and then the expression is evaluated. What is the maximum possible final result that can be achieved?
+\dfrac{\frac{\square}{\square}+\frac{\square}{\square}}{\frac{\square}{\square}}