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cut each paper piece into 5 pieces - IX Mexico Regional Northeast 2010 P1

Source:

September 17, 2022
combinatorics

Problem Statement

Sofia has 55 pieces of paper on a table. He takes some of the pieces, cuts each one into 55 little pieces, and puts them back on the table. She repeats this procedure several times until she gets tired. Could Sofia end up with 20102010 pieces on the table?
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