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More Mixed Fractions

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math
When I first published my solution to the last puzzle, I was led to attempt the expression of all numbers in turn up to 100 by a mixed fraction containing all the nine digits. Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94. Use every one of the nine digits once, and only once, in every case.

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

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