Shared counter in quarto for exercises, examples, etc - r-markdown

Question

I'm using quarto to write an online book and need to mimic the environments and counters of a published book. The latter employs five custom framed environments (examples, exercises, remarks, theorems, definitions) with a joined counter (within the chapter).
In quarto there is very nice infrastructure for creating such cross references for theorems and proofs but they have separate counters. Is it possible to configure/force them to use a joint consecutive counter?
As an example, the following code
The first example is #exm-1.
::: {#exm-1}
This should be Example 1.1.
:::
It is followed by the first exercise, #exr-1
::: {#exr-1}
This should be Exercise 1.2.
:::
is rendered as
The first example is Example 1.1.
Example 1.1
This should be Example 1.1.
It is followed by the first exercise, Exercise 1.1
Exercise 1.1
This should be Exercise 1.2.
Note that the first exercise should receive the number 1.2 (instead of 1.1) because it is the second environment in that chapter.
(Remark: I've also tried to do this via callout blocks as provided through quarto, see Is it possible in quarto to create custom cross-references to callout blocks?.)

Answer 1

Assuming that, you are trying to do this for an HTML book (since you have said online book), we can hack a way to do this using javascript.
At first, we use the example environment #exm in the case of exercises too and also add an additional class name, say .custom like this,
intro.qmd
# Introduction
The first example is #exm-1.
::: {#exm-1}
This should be Example 1.1.
:::
It is followed by the first exercise, [Exercise #exm-2]
::: {#exm-2 .custom}
This should be Exercise 1.2.
:::
It is followed by the first exercise, [Exercise #exm-3]
::: {#exm-3 .custom}
This should be Exercise 1.3.
:::
Note Two things here,
I have used custom reference syntax [Exercise #exm-2] to refer to those exercises, so that they will render as Exercise 1.2 instead of Example 1.2.
Added a class .custom to those example environments which I want to render as Exercise but with the consecutive (shared) counter.
Now since we have used example environments for those with .custom class too, quarto will render those as Example 1.2, Example 1.3, but we need them as Exercise 1.2, Exercise 1.3. So to get them Exercise, we will use javascript on the elements of .custom to simply replace the word Example with Exercise and the counter will remain consecutive since under the hood they are actually example environments.
Therefore, we create an HTML file, say custom.html, and put the necessary javascript code wrapped with script tag into that file,
custom.html
<script>
var custom_title = document.querySelectorAll('.custom .theorem-title');
for (let i = 0; i < custom_title.length; i++ ) {
var mod_name = custom_title[i].innerHTML;
custom_title[i].innerHTML = mod_name.replace("Example", "Exercise");
};
</script>
Then simply add this html file with include-after-body option in _quarto.yaml
_quarto.yaml
project:
type: book
book:
title: "test_book"
author: "Jane Doe"
date: "8/7/2022"
chapters:
- index.qmd
- intro.qmd
format:
html:
include-after-body: custom.html
theme: cosmo
Then if we render the book, this rendered output will look like this,