Counting Covering Triples

★ 7/10combinatorics number theory Counting Modular Arithmetic

Problem

Sets $A, B, C$ satisfy $A \cup B \cup C = \{1, 2, \ldots, 2023\}$ and $A \cap B \cap C = \varnothing$ . Let $n$ be the number of such ordered triples $(A, B, C)$ . Find the last two decimal digits of $n$ .

Answer

Solution

Difficulty	7/10
Topics	combinatorics, number theory, Counting, Modular Arithmetic

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