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Part of 2007 Regional Olympiad of Mexico Center Zone

Problems(1)

convicted person will be released at the top of a 100-step staircase.

Source: Mathematics Regional Olympiad of Mexico Center Zone 2007 P1

11/8/2021
A convicted person will be released when he reaches the top of a 100100-step staircase. But he cannot advance as he pleases, since he is obliged to go up one step each day of the odd-numbered months and go down one step each day of the even-numbered months. If it begins on January 1 1, 20012001, what day will it be released?
combinatorics