I would also like to show you two hats which I purchased in Tibet last September. They are one male and one female, and I assume the only difference between them is the background colour. The male hat is the black one, and the female hat is more colourful.
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HATS FROM TIBET
(MALE HAT - (front))
As you can see from the photos, these Tibetan hats are the same hats, worn by both sexes. They can be worn with the brim down, or turned back.