I am facing a very common issue regarding \"Selecting top N rows for each group in a table\".
Consider a table with id, name, hair_colour, score columns
Use this compound select which handles OP problem properly
SELECT g.* FROM girls as g
WHERE g.score > IFNULL( (SELECT g2.score FROM girls as g2
WHERE g.hair=g2.hair ORDER BY g2.score DESC LIMIT 3,1), 0)
Note that you need to use IFNULL here to handle case when table girls has less rows for some type of hair then we want to see in sql answer (in OP case it is 3 items).