P2911 [USACO08OCT] Bovine Bones G

Bessie loves board games and role-playing games so she persuaded Farmer John to drive her to the hobby shop where she purchased three dice for rolling. These fair dice have $S_1$, $S_2$, and $S_3$ sides respectively ($2 \le S_1 \le 20; 2 \le S_2 \le 20; 2 \le S_3 \le 40$). Bessie rolls and rolls and rolls trying to figure out which three-dice sum appears most often. Given the number of sides on each of the three dice, determine which three-dice sum appears most frequently. If more than one sum can appear most frequently, report the smallest such sum. POINTS: $70$

\* Line 1: Three space-separated integers: $S_1$, $S_2$, and $S_3$.

\* Line 1: The smallest integer sum that appears most frequently when the dice are rolled in every possible combination.

Here are all the possible outcomes. ``` 1 1 1 -> 3 1 2 1 -> 4 2 1 1 -> 4 2 2 1 -> 5 3 1 1 -> 5 3 2 1 -> 6 1 1 2 -> 4 1 2 2 -> 5 2 1 2 -> 5 2 2 2 -> 6 3 1 2 -> 6 3 2 2 -> 7 1 1 3 -> 5 1 2 3 -> 6 2 1 3 -> 6 2 2 3 -> 7 3 1 3 -> 7 3 2 3 -> 8 ``` Both 5 and 6 appear most frequently (five times each), so 5 is the answer.