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All answers having "High points" as clue:

3 Character Answers:

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UPS



4 Character Answers:

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ALPS

JOYS

TORS



5 Character Answers:

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ACMES

MAXES

NOONS

PEAKS



6 Character Answers:

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APEXES

APICES

CRESTS

MAXIMA

SPIRES

TOWERS

UMLAUT



7 Character Answers:

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APOGEES

ZENITHS



8 Character Answers:

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STEEPLES



12 Character Answers:

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CLOTHESHORSE



13 Character Answers:

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REDLETTERDAYS