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All answers having "Squared" as clue:

4 Character Answers:

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EVEN



5 Character Answers:

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CUBED



6 Character Answers:

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EVENED



8 Character Answers:

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EVENEDUP



9 Character Answers:

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SETTLEDUP



15 Character Answers:

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CAESARSCCLXXXIX

HIGHESTSATSCORE

SECONDSINANHOUR