Nope BTW, I posted some reasoning (above) which can speed up brute force methods on the previous page, but it got lost in spam.I'm not sure what's your definition of brute force and I didn't have the patience to read all those responses, but a partial solution is straightforward and allows to find the final result much faster then the actual brute force approach. You only need to notice that the average sum of triple S is 24. This means that the minmax S cannot be smaller than 24, because if any triple has S<=23, then there must be some another triple for which S>=25. Simples! This observation already spares some computational time. Next, you notice that minmax S = 24 would require a uniform S over the whole "ring", because if S = 24 for any triple a, b, c, then the "adjacent" triple must be b, c, a, while you have only one a at your disposal. This makes you start the search from 25 and quickly find the solution.
I think I can guess in what textbook you came across this task and indeed most problems in this field are NP-hard.