Miracles Happen...

Cap with Fold-Up Brim and Multiple-Colored 'Flower' (left)
Cap with Rolled Brim and Flower Made With One (Multi-colored) Yarn (right) 

(Dolls and hats hand made by Sue W. Thompson)

Materials:
1-2 oz yarn for main color (Color A)
less than 1 oz of several other yarns...for 'flower' (Colors B, C, D...as desired for flower)
Size 8 dp knitting needles (#4)
Tapestry needle

Directions:
Cast on 60 sts if using DK or two-ply yarn. Or, cast on 54 sts if using worsted weight or four-ply yarn.
Divide sts evenly between three dp knitting needles.
Being careful not to twist the cast on sts, start knitting in the round as follows:

For cap with Fold-up Brim:

*k2, p1*. Repeat around.
Continue until piece measures about 1" from cast on row.
Continue by knitting each st around until piece measures about 5" from cast on row.

For cap with Rolled Brim:

knit each st until piece measure about 5" from cast on row.

If making cap with multiple-colored 'flower' (See sample cap in photo) -

Change to color B (I generally use green to make it look like 'leaves' or 'petals' beneath the 'flower'.) . Knit each st for about 1".

Change to color C (I generally use a bright 'flower' color'.) Knit each st for about 1".

Change to color D. Knit one row. Cast off.

With tapestry needle and about 15" piece of color B or C, weave yarn through cap, weaving in and out along every knit st around cap...along line of change from Color B to Color C. Pull yarn tight and tie in secure knot. Pull yarn ends to inside of cap and retie in secure knot. Cut ends.

If making cap with single colored 'flower' (See sample cap in photos) -

Continue knitting in main color until about 6" above cast on row.
Change to color B, and knit for about 1¼". Cast off. With about 15" piece of Color B, weave yarn around cap as described above to make 'flower' (along line between colors A and B).

(click on the pictures for a larger view)