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All answers having "Toodles!" as clue:

3 Character Answers:

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BYE



4 Character Answers:

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CIAO

TATA



5 Character Answers:

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IMOFF

SEEYA



6 Character Answers:

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BYEBYE

BYENOW

SOLONG



7 Character Answers:

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CHEERIO



10 Character Answers:

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SEEYOUSOON