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Granny Square Foundations conclusion

Small to Large to Form Corners
  To prepare, count the number of stitches around the edge of the circle. Divide that by four. That will give you the number of stitches for each side. Subtract 6 stitches from that number to allow for the corner building stitches, and the remaining number is the total of SC for each side.

To actually create the Corners: SC across the sides, then work one each: HDC, DC, and TRC. Ch 1 or 2, then TRC, DC, HDC. Finish the side with sc across to the next corner.

For example:
If the number of stitches isn*t divisible by 4, use a decreasing sc to hide those extra sts. Your circle has 32 stitches in it.
Divided by four, that comes to 8 stitches per side. To find the number of stitches per side, you subtract 6 stitches for the corner. For the example: 32 stitches divided by 4 sides is 8 stitches per side.  Subtract 6 stitches that form the corner and that leaves 2 SC for the sides.  This sounds more confusing than it really is.
For a circle with 32 stitches, your pattern would actually read:
Ch 1, sc, hdc, dc, trc, ch 2, trc, hdc, dc, *2sc, hdc, dc, trc, ch 2, trc, dc, hdc. Repeat from * around the square. Connect with beginning ch.
On All other Rounds you will use the SAME size st on the individual rounds.

Struts in the Corners
I call this technique Struts in the Corners because the DC stitches in the corners act like the struts in your car: they suspend, support, and connect the body of the car on top of the frame/wheels.

To prepare, count the number of stitches around the edge of your circle. Divide that by 4. This will give you the number of stitches for each side. Subtract 2 sts per side for the corners, and the remaining number is for the SC down the sides. If the number of  stitches isn*t divisible by 4, you can skip a sc on the sides in row 1, or use a decreasing sc.

For example:
If your circle has 32 stitches, then divided by 4 (sides) gives you 8 sts per side. Subtract 2 sts per side to allow for the corners.

PATTERN INSTRUCTIONS:
For a ring with 32 sts.
Round 1: Ch 1. *6 sc. Ch 2. Dc, ch 2, Dc into same st, ch 2. Repeat from * around circle. Connect with beg ch.
Round 2: Ch 3 (serves as first dc). Work 1 Dc into next 5 Sc. 2 Dc into first ch 2 sp. *(2dc, ch 2, 2dc) into corner ch 2 sp. 2 dc into next ch 2 sp, 6 dc across side. Repeat from * around the square. Connect with beg ch 3, and continue to desired size or end off.

NO SEAM GRANNY SQUARE!
I don't know about you, but I really hate to have that 'seam' in the middle of my granny squares; you know, where the round begins and ends.
This simple pattern eliminates that seam, by starting each round in a corner.
I used worsted weight yarn and an H hook.

Ch 5, connect to form a circle.
Round 1: Ch 5 (1st Dc and Ch 2).  *Work 3 Dc into circle. Ch 2. Repeat from * 2 more times.  Work 2 Dc and connect to beg ch.  Fig. 1.
Round 2: (Ch 3, 1 Dc, Ch 2, 2 Dc) into Ch2 Sp.  *Work 1 Dc into each st. (2 Dc, Ch 2, 2Dc) into corner Ch2 sp. Repeat from * around sides, working 1 Dc beside beg ch, then connect to it.
Round 3: Sl St into Corner Ch2 Sp. (Ch 3, 1 Dc, Ch 2, 2 Dc) into Ch2 Sp.  *Work 1 Dc into each st. (2 Dc, Ch 2, 2Dc) into corner Ch2 sp. Repeat from * around sides, working 1 Dc beside beg ch, then connect to it.
Repeat Round 3 as many times as needed to complete a granny square of your desired size.
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NO SEAM!
Granny
Fig. 1
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Pg1     Pg2       Pg3
Abbreviations:  
Beg: Beginning
 Ch: Chain stitch
Dc: Double Crochet   
Sc: Single Crochet  
Trc: Treble Crochet
Lp: Loop  
Hk: Hook
 Sk: skip stitches
Sl St: slip stitch
Yo: Yarn Over hook