okay, so I will do my best to explain how I made this. I have never written a crochet pattern, so someone familiar with following a lot of crochet patterns may think I did it all wrong, but I will try to at least help you get the end result, without too much confusion.
I used a size k crochet hook, but you can fiddle with it, I probably wouldn't go smaller, because the flower will get smaller as you go to a smaller hook. I have not tried a bigger one, it may produce a fuller looking flower, but it may have too much "empty space" if that makes sense.
you can use any yarn you want, I always thought the fuzzy yarn would look cute, but I have a hard time seeing one crochet from the next when I try, so I took the easy way out. (By the way, I just used 100% cotton, worsted weight 4-ply yarn)
First, ch. 5 and slip stitch to form a ring
ROUND 1:ch 1, work 9 sc into the ring, join with a sl. st. in first sc to form a ring
ROUND 2: ch 1, 2 hdc into each sc around (18 hdc), join in first dc
ROUND 3: ch 1, sc into each hdc around (18 sc), join in first sc
ROUND 4: ch 1, 2 hdc into each sc around (36 hdc), join in first hdc
the end result should look like this
next, ROUND 5: ch 1, sc in same hdc as joining, *ch 6, sk next 5 hdc, sc in next hdc; repeat from * 4 times more, ch 6 sk next 5 hdc, join with sl st in first hdc (6 ch 6 sps)
it should look like this
ROUND 6: in first ch 6 sp, (sc, hdc, dc, 3 tr, dc, hdc, sc), repeat in all 6 ch 6 sps, join to first sc
Next, I don't really know what this is called, but I slip stitched vertically down until I reached round three (about three sl sts)
ROUND 7: ch 1, sl st around post of sc on round 3, *ch 3, skip next 2 sc on round 3, repeat from * 4 times, ch 3 skip next 2 sc on round 3 join with a sl st on first sc (6 ch 3 sps)
in first ch 3 sp (sc, hdc, 3 dc, hdc, sc) repeat in all ch 3 sps, join and fasten off
your flower should look like this
I make 10-12 flowers (you decide how long you want the scarf, try it on and tie it how you like to decide length) on the last two scarves I made, I just got a needle and matching thread and sewed the flowers together, petal to petal, by hand. On the second one I made, I crocheted the flowers together, petal to petal, usling a slip stitch (this worked fine, but took a long time). On the first one I made, I crocheted a back piece (by doing rows of 8 hdc, ch 1, and turning). Then (having left a long tail in each flower) wove the flowers onto the back piece with my crochet hook. I liked the fullness of the first scarf the best, and since it looked more full, I only made a single layer flower for each flower, rather than a double. However, this took me a really long time to make the back piece, and a lot of yarn, so that is why I have by passed it on the other three scarves. I made 12 flowers on the first scarf too, 11 on the 2nd and 3rd, and only 10 on the last one. I also did 7 petals on the first 3 and only 6 on the last one (I am still trying to figure out the best pattern, one that looks good, but doesn't take forever to make). I can make about 3 of the flowers shown in this post in one hour, to give you an idea
this is a very forgiving pattern, it doesn't matter if all your flowers are slightly different, or if one of your rows ends up with more crochets than it should, just adjust your pattern and keep going. Once the flowers are all hooked together, you can't tell where mistakes are. Also, it doesn't really matter if you can, because the flowers don't need to look exactly alike. Just use this pattern as a guide line, figure out what works for you, where I made mistakes (or where I wrote the pattern confusing) and just dive in a try.