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All answers having "Type of hat" as clue:

4 Character Answers:

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HALO



5 Character Answers:

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BERET

DERBY

OPERA

STRAW

TOQUE



6 Character Answers:

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ATLAST

BRETON

COOLIE

FEDORA

PANAMA

SLOUCH

TOPPER

TRILBY



7 Character Answers:

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PORKPIE

TRICORN



11 Character Answers:

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DEERSTALKER