How Many Stitches Are in a Shawl with 42 Teeth in Knitting?

[Kzz]

Hope this is the right place to post, my girlfriend asked me how many Stich she did use when
she started with one stitch. In each row there is one more stitch and in every 8th row there are 5 stitches fewer... how many stitches did I knit in total, when the shawl has 42 of those teeth which I make, when I increase those 5 stitches every 8th row?

And how do you calculate it?

 

[jvicens]

Hello,

Thank you for posting your question here. I am happy to help you with this knitting problem.

To answer your first question, we will need to use some basic mathematical principles. Let's break the problem down into smaller parts to make it easier to understand.

First, we know that your girlfriend started with one stitch and in each row, she added one more stitch. This means that in the first row, she had one stitch, in the second row she had two stitches, in the third row she had three stitches, and so on. We can represent this pattern with the formula n + 1, where n is the row number.

Next, we know that in every 8th row, she decreased 5 stitches. This means that in every 8th row, she had 5 stitches less than the previous row. We can represent this pattern with the formula n - 5, where n is the row number.

Now, we need to find the total number of stitches in the shawl with 42 teeth. Each tooth consists of one increase and seven rows of knitting, which means that each tooth adds 8 stitches to the total count. So, we can represent the total number of stitches with the formula 8n, where n is the number of teeth.

Using these formulas, we can create an equation to solve for the total number of stitches:

8n = (n + 1) + (n + 2) + (n + 3) + ... + (n + 8) - 5 - 5 - 5 - ... - 5 (repeating 5 for every 8th row)

We can simplify this equation to:

8n = 8n + 36 - 5x (where x is the number of times 5 is subtracted)

Now, we can solve for x by setting it equal to the number of teeth, which is 42:

42 = 8n + 36 - 5x

Subtracting 36 from both sides, we get:

6 = 8n - 5x

We can see that this equation has multiple solutions, but the simplest solution is when n = 1 and x = 2. This means that your girlfriend started with one stitch and decreased 5 stitches in the 8th and 16th row, resulting in a shawl with 42 teeth and a total of (8 *