Sticky Problem and a Super-Math-Rich Post

I just moderated a comment from a listener that said she had to put 41 yarn-overs into 267 stitches evenly. She fudged it. I'm going to say she would have to - it averages to one yarn-over about every 6.5 stitches. This is nearly impossible, really. If I were working some other increase, say, a lifted increase, I would say, just do an *increase, work 6 stitches, increase, work 7 stitches* repeat, and it should even out. I think that would drive me nuts when making eyelets, since my switching between 6 and 7 stitches apart would be obvious, to me, at least.

A possible solution: factor your numbers out and look for common factors. The major issue of this is that 41 is a prime number, which means that we would have to add or subtract somewhere to make this work.

267 is not a prime number, so we can take it apart and see what we have. Unfortunately, we don't have far to go.

267 = 89 * 3

89 is a prime number. Luckily, 3 * 14 = 42. So, we could round 41 to 42 by deciding that one more increase in the mix is better than the crazy-making idea above.

We can mentally, and with stitch markers, divide our work by three - so we're facing putting 14 eyelets into 89 stitches. 14 * 6 = 84, which leaves us with 5 extra stitches for each "wedge" of 89, if we increase every six stitches.

Speaking of which, to increase every six stitches *really* evenly, we would do this:
(x = stitch, o = increase)
(stitch marker) xxx o xxxxxx o xxxxxx o xxxxxx o xxxxxx o xxx...

I'm not going to do it 14 times, but you get the idea.

What do we do about those extra 5 stitches? We could put them in-between wedges, so that at some point, our work will look like this:
o xxxxxx o xxxxxx o xxxxxxxx(stitch marker)xxx o xxxxxx o xxxxxx

Which is to say, that, around our stitch markers, we would have 5 + 6 = 11 stitches as spacers. You could, and I would, decide that this is a design feature and only have to decide where they should lie - it doesn't even have to be 100% evenly, but I would probably put two of them under the arms of a sweater and the third in the middle of the back or front.

Design Feature Solution #2:
Break the set of 42 increases into 3 sets of 14 stitches.

267 / 14 = just over 19.
So, the first set of eyelets will be an increase every 19 stitches.
Total stitches = 281

281 / 14 = just over 20.
The second set could be every 20 stitches.
Total stitches = 295 stitches

295 / 14 = just over 21
The second set could be every 21 stitches.
Total stitches = 309 stitches

So, by adding one total stitch, and I'm not going to try to draw it for you, you could have a perfectly neat little leaning line of yarn-overs, in either 3 rows or 6, depending on how you do it. You could even stagger them by as much as you like, by making your first increase sooner than you would, and letting the stitches fall where they will.

I recorded my show on grafting, but have not knit, grafted, or photographed it, so it is still in the works, so to speak. I may talk about the above math in my next show, because I don't think a lot of you read this blog. Am I wrong? Leave me a comment to prove it. :)