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All answers having "Admits" as clue:

4 Character Answers:

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LETS

OWNS



5 Character Answers:

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AVOWS

CEDES



6 Character Answers:

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COPSTO

FESSES

LETSIN

LETSON

OWNSUP



7 Character Answers:

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ACCEPTS



8 Character Answers:

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ALLOWSIN

CONCEDES

OWNSUPTO

RECEIVES