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All answers having "Discarded" as clue:

3 Character Answers:

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GEM



4 Character Answers:

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SHED



6 Character Answers:

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DUMPED

UNKEPT



7 Character Answers:

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CASTOFF

OFFCAST



8 Character Answers:

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OBSOLETE

REJECTED

SCRAPPED



9 Character Answers:

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TOSSEDOUT



10 Character Answers:

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THROWNAWAY