Find Tuong's minimum

Algebra Level 5

Let \(x, y,z\), and \(t\) be positive real numbers such that \(x + y + z + t = 1\). What is the minimum value of

\[\frac{1}{x} + \frac{1}{y} + \frac{4}{z} + \frac{16}{t}?\]

This problem is posed by Tuong N.

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