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Cut the perfect square out

Source: CSMO 2019 Grade 11 Problem 3

July 30, 2019
combinatorics

Problem Statement

nn symbols line up in a row, numbered as 1,2,...,n1,2,...,n from left to right. Delete every symbol with squared numbers. Renumber the rest from left to right. Repeat the process until all nn symbols are deleted. Let f(n)f(n) be the initial number of the last symbol deleted. Find f(n)f(n) in terms of nn and find f(2019)f(2019).
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