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100 people came to party - All-Russian MO 2003 Regional (R4) 9.5

Source:

September 17, 2024
combinatorics

Problem Statement

100100 people came to the party. Then those who had no acquaintances among those who came left. Among those who remained, then those who had exactly 11 friend , also left. Then those who had exactly 22, 33, 44,.. . . , 9999 acquaintances among those remaining at the time of their departure did the same..What is the largest number of people left at the end?
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