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how many trilegal numbers with 10 digits?

Source: Brazilian Mathematical Olympiad 2024, Level 2, Problem 4

October 12, 2024
number theorycombinatoricscounting

Problem Statement

A number is called trilegal if its digits belong to the set {1,2,3}\{1, 2, 3\} and if it is divisible by 9999. How many trilegal numbers with 1010 digits are there?
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