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All answers having "Essential part" as clue:

4 Character Answers:

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CORE

CRUX

GIST

MEAT

PITH

ROOT

YOLK



5 Character Answers:

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HEART



6 Character Answers:

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KERNEL

MARROW



8 Character Answers:

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MAINSTAY



10 Character Answers:

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SINEQUANON



15 Character Answers:

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MEATANDPOTATOES