Was watching a TED-Ed video that posed this Cheating Royal 'Riddle'. The answer is 385, because the other 3 are clearly disqualified (840 and 423 are impossible answers, 700 is the highest possible score from 20 rolls which is highly improbable)

This got me questioning how you would go about calculating what would be the highest possible number that was only 10% likely, and not higher. Essentially, if you took a full data set of all of the possible sums of rolling these dice 20 times, what number is the cutoff for the top 10 percent, and how would I calculate that?