Question: I have been reading this [article](https://css-tricks.com/how-nth-child-works/) and it is pretty clear to me so far that something along the lines of: `ul li:nth-child(3n+3)` will select every 3rd `li` due to the fact that the "n" within the expression starts at zero and then represents a set of all positive integers; so n = 0, n = 1, n = 2, etc., which in the article I have linked goes on to indicate that indeed `:nth-child(3n+3)` is tantamount to (3x0)+3 which equals 3, (3x1)+3 equals 6 and so on. I have also seen similar CSS such as: `.some-selector:nth-child(1n); .some-selector:nth-child(2n);` 
What I glean from the examples from the aforementioned article leads me to posit that `.some-selector:nth-child(1n);` would equate to `.some-selector:nth-child(0);` but this also feels wrong to me. Can someone help me to better understand this? Thanks

Answer: 
`Xn` essentially means every Xth child, where `Xn+Y` is every Xth child with an offset of Y.

`1n` is quite nonsensical, as it will just select every child (every 1th child, which essentially is just every child).

```css
div:nth-child(1n)
{
  color: red;
}
```

```html
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
```

`2n` would be every 2nd child, starting with the second child ([0], 2, 4, 6, 8, 10, ...). Technically this would start with the zeroth child, but [there is no such thing in HTML/CSS](https://softwareengineering.stackexchange.com/questions/314537/why-does-nth-child-in-css-start-from-1-instead-of-0), so it's functionally equivalent to `2n+2`.

```css
div:nth-child(2n)
{
  color: red;
}
```

```html
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
```

`2n+1` would be every 2nd child, starting with the first child (1, 3, 5, 7, 9, ...).

```css
div:nth-child(2n+1)
{
  color: red;
}
```

```html
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
```

You can specify any Y value in `Xn+Y`, so if you wanted your every-other selector to start with the 4th element, it would be `2n+4`

```css
div:nth-child(2n+4)
{
  color: red;
}
```

```html
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
```

You can also specify a number in `nth-child` to directly select whichever child you want.

```css
div:nth-child(4)
{
  color: red;
}
```

```html
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
<div>Hi</div>
```
Your feeling is correct, `:nth-child(1n)` does not equal `:nth-child(0)`. A selector with an expression like `:nth-child(1n)`, or actually `:nth-child(n)` which is the same would select all children. So apparently it wouldn't make much sense...

To understand which elements are going to be selected you have to give `n` incremental values starting from 0, as in the table in the article you linked, and all the values you get will be the indexes of the selected elements.

There are also some [:nth Testers](https://css-tricks.com/examples/nth-child-tester/) that will help you understand better.