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Ladder game, victory if you get the zero ladder

Source: Mexico National Olympiad Mock Exam (OMMock) P5

November 9, 2020

combinatoricsgame strategy

Problem Statement

A ladder is a non-decreasing sequence

a_1, a_2, \dots, a_{2020}

of non-negative integers. Diego and Pablo play by turns with the ladder

1, 2, \dots, 2020

, starting with Diego. In each turn, the player replaces an entry

a_i

a_i'<a_i

, with the condition that the sequence remains a ladder. The player who gets

(0, 0, \dots, 0)

wins. Who has a winning strategy?
Proposed by Violeta Hernández