There are 10 multiple-choice questions, each of which has 4 options $A, B, C, D$.
There is only one correct answer. 1 point is awarded for the correct answer, and 0 points for the wrong answer.
let $\vec{s_i}$ represents the options for a trial, and $S_i$ represents the score for that trial.
Given $n$ historical trial results, how to choose options for this trial to maximize score expectations?
I presume you are only given the total score for each trial, not the scores on individual questions.
There are $4^{10} = 1048576$ possible ways to choose an answer for each question.
It's a large number if you're working by hand, but not much for a computer. So you just check which of these produce the observed results on the historical trials, and of those that do choose one at random.