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All answers having "Cheerio!" as clue:

3 Character Answers:

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RHO



4 Character Answers:

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TATA



5 Character Answers:

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ADIEU

ADIOS

SEEYA



6 Character Answers:

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PIPPIP



7 Character Answers:

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TOODLES



8 Character Answers:

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FAREWELL

TOODLEOO