In a post, the following question was posed:

We can select unique values \(\displaystyle\frac{1}{i}\) for \(i=1,\dots,n\). Find all combinations that add up to 1.

A complete enumeration scheme was slow even for \(n=10\). Can we use a MIP model for this or something related?

A single solution is easily found using the model:

Mathematical Model |
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\[ \begin{align} & \sum_{i=1}^n \frac{1}{i} \cdot \color{darkred}x_i = 1 \\ & \color{darkred}x_i \in \{0,1\} \end{align}\] |