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Ways to score 42 with 3 rolls of a 20 sided dice

Source: Bangladesh Mathematical Olympiad 2021 Problem 5

February 20, 2022
combinatorics

Problem Statement

How many ways can you roll three 20-sided dice such that the sum of the three rolls is exactly 4242? Here the order of the rolls matter. (Note that a 20-sided die is is very much like a regular 6-sided die other than the fact that it has 2020 faces instead of 66)