OMCPLP 2022 Problem 6
- Day 2
A necklace contains 2024 pearls, each one of them having one of the following colours: black, green and yellow. Each moment, we will switch each one of all pearls simultaneously to a new one following the following rules:
i) If its two neighbours are of the same colour, then it'll be switched to that same colour. ii) If its two neighbours are of different colours, then it'll be switched to the third colour.
a) Does there exist any necklace that can be transformed into a necklace that consists of only yellow pearls if initially half of the pearls are black and the other half is green?
b) Does there exist a necklace that can be transformed into a necklace that consists of only yellow pearls if initially 998 pearls are black and the rest 1026 pearls are green?
Dataset text AI-MO AoPS. Quoted with source.
Solutions
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