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All answers having "Hearts" as clue:

4 Character Answers:

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GAME

NUBS

SUIT



5 Character Answers:

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ACEOF

AFIRE

CORES

GISTS

PITHS

PUMPS

ROOTS



6 Character Answers:

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MIDSTS

ORGANS



7 Character Answers:

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CENTERS



8 Character Answers:

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CARDGAME

ESSENCES