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[IMONST2 2022 Primary #2] Number sequence

Source:

July 4, 2023
combinatorics

Problem Statement

The following list shows every number for which more than half of its digits are digits 22, in increasing order: 2,22,122,202,212,220,221,222,223,224,…2, 22, 122, 202, 212, 220, 221, 222, 223, 224, \dots If the nnth term in the list is 20222022, what is nn?
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