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All answers having "Contests" as clue:

4 Character Answers:

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BEES

VIES



5 Character Answers:

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AGONS

BOUTS

DUELS

GAMES

MEETS

RACES



6 Character Answers:

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ARGUES

DENIES

EVENTS



7 Character Answers:

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OPPOSES



8 Character Answers:

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PAGEANTS



9 Character Answers:

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RIVALRIES