Given that three positive integers $$A$$, $$B$$, and $$C$$ (the numbers can be the same), and $$A+B+C=31$$, find the largest value of $$A\times B\times C$$. 
Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations