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For this one I am using a G hook, and Vannas Choice so it's a little softer for a newborn baby.
FOR BRIMMED HAT
Rnd 1) ch2, 11hdc in second ch from hook, sl st to top of first hdc (11hdc)
Rnd 2) ch1, 2hdc in same st and in each st around, sl st to top of first hdc (22hdc)
Rnd 3) ch1, 2hdc in same st, 1hdc in next st, * 2hdc in nest st, 1hdc in nest st, repeat from * around (33hdc)
Rnd 4) ch1, 2hdc in same st, 1hdc in next 2stS, * 2hdc in next st, 1hdc in next 2sts, repeat from * around (44hdc)
Rnd 5) ch1, 2hdc in same st, 1hdc in next 3sts, * 2hdc in next st, 1hdc in next 3sts, repeat from * around (55)
Rnd 6-13) ch1, hdc in same st and in each st around, (55hdc)
Rnd 14) ch1, sc in same st and in next 14sts, 2hdc in next st, * hdc in next st, 2hdc in next st, repeat from * 5 more times, sc in next st and in each st to end of row, sl st to top of first sc,
Rnd 15) ch1, sc in first st and in next 14sts, hdc across next 20 hdc, sc in next st and in each st across, sl st to top of first sc
Rnd 16)ch1, sl st in first st and in next 14sts, hdc in next 20hdc, sl st in each st across to end of rnd, sl st to close. fasten off and weave in ends.
Optional strap with buttons:
Rnd 1)ch22, 2sc in second ch from hook, sc across to last ch, 3sc in last ch, working on opposite side, sc across to end, 1sc in same ch as first 2sc.
Rnd 2)ch1, sc in same st, 2sc in next st, sc across to set of 3sc, (2sc in first st, sc next st, 2sc in third st) sc across to last st, 2sc in last st, fasten off. Attach to hat with buttons
FOR NOT BRIMMED
Work same as above to rnd 13, Rnds 14+15, repeat rnd 5
Rnd 16) sl st or sc around to finish off.
Changing colors as you like.
I used ravelry to find a flower to attach to two of them. Or you can google free crochet flower pattern.