Sometimes called an afterthought thumb, I first read about it in Elizabeth Zimmermann's Knitter's Almanac.
I really like this method because it's seamless; sometimes when patterns have you place stitches on a holder and then cast on the top stitches you can get an odd seam right in the crease where your thumb meets the hand, and that can be uncomfortable.
The only trouble that some people may have with this method is that you cannot immediately try on your mitten in progress, as you can with mittens where the stitches are put on holders. But if you want to you can just knit a few more rows and then pick up the stitches instead of waiting until the mitten is done, threading the waste yarn through them so you can try on your mittens as you knit.
The trick:
Knit to where you want to place the thumb hole, and take a length of contrasting yarn, and knit the thumbhole stitches with it instead of your working yarn:
(see the working yarn, still on the right-hand side of the work?)
Then, slip all these stitches back onto your left hand needle purl wise:
And knit across them, with your working yarn:
Here are the held stitches after a few rows have been worked:
(Fetching uses a ribbed pattern. When knitting with the waste yarn, just knit plainly, and when knitting back across the waste yarn, knit plainly again, then pick up any stitch patterns again once you've passed the thumb. If using colour patterns, they can be resumed right away as you are knitting over the waste yarn. It is just easier to pick up the stitches later if they are all knit.)
Finish the mitten, and then turn it inside out:
See the purple bumps in-between the blue bumps? Those are the stitches you'll be picking up.
Start picking up the stitches using a pair of circular needles:
As it begins to get awkward to fit them on the needle, slide them onto the cord and continue picking up all along the top edge:
When you get to the end of the row, there will be a stitch where the waste yarn only holds half of it; you want to pick that stitch up too:
Then just turn the work upside down, and keep picking up the underside stitches too:
Keep a loop of the circular cord at the end, to separate the two sides.
Here it is with all the stitches picked up:
The top row will have one more stitch than was originally knit onto the waste yarn, and the bottom should have as many as was originally knit.
Usually, patterns will say that after picking up stitches you'll have one side equal, and one side with one less stitch, but I find that the method I use results in fewer holes.
Now, start puling out the waste yarn, with no worries of a dropped stitch, since they are all already on the needles!
Here it is with the waste yarn removed, and all the now live stitches on the needles:
Pull the cord of the needle until there isn't a loop at the end anymore:
Stick the needles into the thumb hole and out of the mitten:
(The fetching are open at the top, so I stuck them out the top, if making a closed top mitten, just send them out the wrist.)
And pull them out, flipping the mitten right side out in the process:
Ta da! You are almost ready to start knitting your thumb!
I like to make sure the top and bottom are equal in stitch count, and it really helps to tighten things up and prevent holes if one more stitch is picked up and put on bottom needle:
If things are still a bit loose at the sides of the thumbhole, just pick up one more stitch at each end and knit it together with the next stitch on each needle on your first round.
From here you can either move all the stitches to DPNs or you can keep up with the circulars and knit the thumb magic loop style.
Knit your first round through the back loop for extra security and tightness, to further help prevent holes.
If doing colour work that requires a certain number of stitches, simply decrease or increase evenly along your first row to achieve that number.
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