Predicting with Most Coverage

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I would just like some guidance here as to what field of math or theorem to look into. I have a problem where I am trying to predict the optimum solution. I have n tries to guess the solution where m is the total number of possible solutions and n is less than m. How would I go about creating n solutions that have the best chance to cover the best solution given that my predictions for the solutions are as accurate as possible? I don't need an answer necessarily. Just any reference to where I might be able to research the subject would be great.

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You may find decision theory useful. It includes the study of how to make the best choices under uncertainty.

https://en.wikipedia.org/wiki/Decision_theory