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2019 Discrete Tiebreaker #2

Source:

October 5, 2022
2019Discrete Math Tiebreaker

Problem Statement

Let P1,P2,,P720P_1,P_2,\dots,P_{720} denote the integers whose digits are a permutation of 123456123456, arranged in ascending order (so P1=123456P_1=123456, P2=123465P_2=123465, and P720=654321P_{720}=654321). What is P144P_{144}?