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5

Part of 2020 OMMock - Mexico National Olympiad Mock Exam

Problems(1)

Ladder game, victory if you get the zero ladder

Source: Mexico National Olympiad Mock Exam (OMMock) P5

11/9/2020
A ladder is a non-decreasing sequence a1,a2,…,a2020a_1, a_2, \dots, a_{2020} of non-negative integers. Diego and Pablo play by turns with the ladder 1,2,…,20201, 2, \dots, 2020, starting with Diego. In each turn, the player replaces an entry aia_i by ai′<aia_i'<a_i, with the condition that the sequence remains a ladder. The player who gets (0,0,…,0)(0, 0, \dots, 0) wins. Who has a winning strategy?
Proposed by Violeta Hernández
combinatoricsgame strategy