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To make this hat you need to know how to make a FPdc (Front Post double crochet). What you do is work a double crochet around the post of the stitch below, instead of working into the loops on top of the stitch.
this hat is extremely adaptable in terms of size (make a number of rounds until the size is right for the crown of the head, hat size), and for types of yarn and hook size. use a hook of the right size for the yarn you have, and work a number of rounds increasing each round until you have the size crown hat you want, then continue making rounds without increasing, until you have the length you want for the hat.

start by making a chain of 5 (adjust number to be just right for a ring to contain 12 dc). join together with a slip stitch in first stitch, making a ring.

round 1: chain 3 (counts as first dc here and throughout). dc 11 times into ring, for a total of 12 dc.

round 2: chain 3, dc into next dc of round below, FPdc around post of same dc (increase made), *dc into next st, FPdc around post of same dc*, continue from * to * around, join with slip stitch in top of beginning ch-3. 24 stitches.

round 3: ch 3, dc into next st, dc into next 2 sts, FPdc around FPdc of round below (increase made), *dc into next 2sts, FPdc around FPdc of round below* . Continue repeating from * to * around, join with slip stitch in top of beginning ch-3. 36 stitches.

Continue with  increase pattern until the top of the hat is of the desired diameter, for the crown of the hat. Then you continue in the same pattern, but without increases, and by alternating dc and FPdc around, to make a ribbing pattern. After the first row without an increase, continue in pattern always making dc into dc and FPdc around FPdc. When the hat is the length desired, fasten off!

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