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All answers having "Competition" as clue:

4 Character Answers:

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GAME

MEET

RACE



5 Character Answers:

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EVENT

MATCH



6 Character Answers:

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STRIFE



7 Character Answers:

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CONTEST

RIVALRY

TOURNEY



8 Character Answers:

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THELISTS



9 Character Answers:

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CUTTHROAT



10 Character Answers:

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TOURNAMENT