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All answers having "Persevered" as clue:

3 Character Answers:

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WON



6 Character Answers:

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HELDON

HUNGON

KEPTON



8 Character Answers:

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INSISTED

KEPTATIT

PUSHEDON



9 Character Answers:

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CARRIEDON

PRESSEDON



15 Character Answers:

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STAYEDTHECOURSE