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2021 chips of each of 2021 colors

Source: Spain Mathematical Olympiad 2021 P3

May 10, 2021
combinatoricsSpainParity

Problem Statement

We have 20212021 colors and 20212021 chips of each color. We place the 202122021^2 chips in a row. We say that a chip FF is bad if there is an odd number of chips that have a different color to FF both to the left and to the right of FF.
(a) Determine the minimum possible number of bad chips.
(b) If we impose the additional condition that each chip must have at least one adjacent chip of the same color, determine the minimum possible number of bad chips.
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