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If the pattern requires only a couple large panels of color variation, one can probably get by with just using yarn skeins. However, if there will be several color changes in a row, an adequate supply of bobbins should be purchased to wind yarn colors onto. Trying to use many skeins at once will result in a dreadful tangle.
While working the foundation row of colors, just add in each color from a bobbin/skein, keeping them at the back of the work. On subsequent rows where the colors are already established, at each color border, lift the just-used yarn/bobbin up (Fig.1), pass the next yarn/bobbin under it (Fig.2), lower the just-used yarn/bobbin (Fig.3), commence knitting off the next yarn/bobbin (Fig.4) with adequate tension. By so doing, the yarns have been crossed at the color border. This will form a nice little locking weave at the back of the work along each color border, thus holding the color panels together.
In The Round: Intarsia cannot be worked in the round as a continuous knit; it is strictly a back-and-forth knitting method. Unlike other sock-types, argyle socks are usually knitted flat and seamed, as is the case with the TKGA Level II (2) sock. Intarsia can be worked in the round with a bit of ingenuity, but it is still worked back and forth (K one round, P one round), as follows:
Work on DP or circular needles. Be sure to mark the beginning/end of round. Don't place it between two needles; use a marker. Place and add in your colors as you would for flat intarsia knitting.
Knit Round: YO, knit around to last stitch before YO. Sl 1, K 1 (the YO), PSSO (or however you wish to achieve a left-slant decrease). Turn.
Purl Round: YO, purl around to last stitch before YO. Purl last stitch and YO tog. Turn.
The reason for choosing a left slant decrease is that it causes the ending knit stitch to cover over the YO on the knit rows--much more appealing than the alternative.
Be sure to practice this before actually applying it.