Maths Olympiad Prep

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Combinatorics Difficulty 5.0 AIME, harder Find the answer United Kingdom

A total of 2021 coloured koalas are arranged in a row and are numbered from 1 to 2021. Each koala is coloured red, white or blue. Amongst any three consecutive koalas, there are always koalas of all three colours. Sheila guesses the colours of five koalas. These are her guesses: Koala 2 is white; Koala 20 is blue; Koala 202 is red; Koala 1002 is blue; Koala 2021 is white. Only one of her guesses is wrong. What is the number of the koala whose colour she guessed incorrectly?

(A) 22 (B) 2020 (C) 202202 (D) 10021002 (E) 20212021

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