Math: it really works!

I've been working away on the Highlighter shawl (between commissioned design projects, because a girl's got to make a living)...

I knew I was getting to close to the end last night, and about 9pm, I hit a crossroads.

The way the shawl pattern works is that you have to finish the patterned section on Row 1 of a 10-row pattern. And then there's 6 rows of edging and a bind-off.

I was at Row 1, and there was about 15gms (my digital scale was flickering between 14 and 15) of yarn left. I had to whether I had enough for an additional 10 pattern rows and 6 edging rows plus bind-off, or whether I should just forge ahead with the edging.

So I did what any mathematically inclined knitter would do: I open up a spreadsheet application on my laptop and did some calculations.

I knew the skein was 115gms. I had 15 left, so I'd used 100gm. And I knew how many stitches I'd worked with that 85gms....

The shawl starts with 1 stitch, and increases 1 st every other row. And at that point I had 139 sts.

So I calculated that I had worked 19,321 sts. Yes, really.

Here's how that goes:
I cast on 1 st, and worked 1 row on that 1 st. So that's 2 sts, worked over 2 rows.
I increased to 2 sts, and then worked back over those 2 sts. So that's 4 more, for a total of 6, worked over 4 rows.
I increased to 3 sts, and then worked back over those 3 sts. So that's 6 more, for a total of 10, worked over 6 rows.
I increased to 4 sts, and then worked back over those 4 sts. So that's 8 more, for a total of 18, worked over 8 rows.

You see the pattern?

I had 139 sts, and I'd just finished a right side row. So I'd worked 2 rows at 1 st, 2 rows at 2 sts, 2 rows at 3 sts, 2 rows at 4 sts, .... 2 rows at 138 sts, and then just one row at 139 sts (hadn't yet worked the WS row back). Which is 2 x (1 +2 + 3  + 4 + 5.... 138) + 139.

And that's 19, 321. At 100gms of yarn, that's 193 sts per gm. And I've got 14 or 15gms left, so best case, that's 15 x 193 sts = 2898 sts worth of yarn left, worst case that's 2705 sts.

To work the additional repeat and the edging, I'd need to be able to work
139 + 2 x 140 + 2 x 141 + 2 x 142 + 2 x 143 + 2 x 144 + 145 for the pattern repeat (since the pattern ends after a RS row), and then 6 rows at 144 sts for the 6 edging rows (there are no increases in the edging), and then the bind off.  That's 2279 sts for the pattern repeat and edging rows. And then because I need to work a loose BO, let's assume that I need about one and a half times the usual row's worth of yarn for the BO, so that's another 216 sts worth of yarn.

So in total, I needed 2,495 sts worth of yarn. Even with a little bit of rounding error, I figured I could just make it.

I'm a brave? foolhardy? trusting type, so I forged ahead. I weighted the yarn as I went, to track usage, and knitted gamely on.

And then I was done.

Indeed, I just made it. It's closer than I would have liked, but I got there.