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All answers having "Offer" as clue:

3 Character Answers:

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BID

LAY



4 Character Answers:

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GIVE



5 Character Answers:

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PUTIN



6 Character Answers:

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EXTEND

HITMAN

SLAYER

TENDER



7 Character Answers:

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PRESENT



8 Character Answers:

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ASSASSIN

BIDPRICE

FRACTURE

OVERTURE

PROPOSAL