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Ok, after hours trying to actually understand the problem, and after trying to solve it in reverse, I hope to bring some clarity for those who are having a hard time trying to solve or to understand what exactly needs to be done and what the codes posted here are actually doing. I did this using Python 3.

Ignoring the mathematical terms, the problem wants you to create a list in a concise way (that's called 'List Comprehension'). Which consists on creating a list using 'for' and, possibly, 'if' (in case you want an extra condition in that list).

In this case, it asks you to create multiple lists using 3 'for' clauses: i, j and k. In each theses clauses you will choose an range to vary from 0, which will be called x (for clause i), y (for clause j) and z (for clause k).

The challenge here is to create every possible list that will show all values from the chosen ranges (x, y and z) in a way that the the predecessor number will change to the next value from the range only AFTER the successor number shows all it's values first.

Before trying an example, first a reminder:
As seen in previous challenges, in a 'for' clause, the value of a range will vary (as a standard) from 0 to the predecessor number in that range. I.E.: for A in range(2): will output 0 and 1, but not 2.

Now, let's try to solve it with a simple example: I'll set both, x, y and z to 1, just to make it easier.

This is the formula in a clearer way (not in a single line, but I believe it's best for beginners to understand):

As you can see, it made 8 different output variations.

Now, to the last part of the problem...
It creates one extra condition: it will NOT print the outputs which the sum of the values inherited by i, j and k equals to the integer 'n'.

That's an extense explanation, but I'm just trying to make it as clear as possible for those who, just like me, are having a hard time figuring out what the problem wants and what the codes posted here and in the examples are really doing. Hope it helps someone.

## List Comprehensions

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Ok, after hours trying to actually understand the problem, and after trying to solve it in reverse, I hope to bring some clarity for those who are having a hard time trying to solve or to understand what exactly needs to be done and what the codes posted here are actually doing. I did this using

Python 3.Ignoring the mathematical terms, the problem wants you to

create a list in a concise way(that's called 'List Comprehension'). Which consists oncreating a list using 'for' and, possibly, 'if'(in case you want an extra condition in that list).In this case, it asks you to create multiple lists using 3 'for' clauses: i, j and k. In each theses clauses you will choose an range to vary from 0, which will be called x (for clause i), y (for clause j) and z (for clause k).

The challenge here is to create every possible list that will show all values from the chosen ranges (x, y and z) in a way that the the predecessor number will change to the next value from the range only AFTER the successor number shows all it's values first.

Before trying an example, first a reminder:As seen in previous challenges, in a 'for' clause, the value of a range will vary (as a standard) from 0 to the predecessor number in that range. I.E.: for A in range(2): will output 0 and 1, but not 2.Now, let's try to solve it with a simple example: I'll set both, x, y and z to 1, just to make it easier.

This is the formula in a clearer way (not in a single line, but I believe it's best for beginners to understand):

(copy and paste the code in an code editor for clearer reading)In the example above, that's what will happen behind the scenes, in this exact order:

i = 0, j = 0, k = 0

i = 0, j = 0, k = 1

i = 0, j = 1, k = 0

i = 0, j = 1, k = 1

i = 1, j = 0, k = 0

i = 1, j = 0, k = 1

i = 1, j = 1, k = 0

i = 1, j = 1, k = 1

It will print exactly like that:

`[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1], [1, 1, 0], [1, 1, 1]`

As you can see, it made 8 different output variations.

Now, to the last part of the problem...It creates one extra condition: it will NOT print the outputs which the sum of the values inherited by i, j and k equals to the integer 'n'.So, this time, the code will become:

In this case, let's suppose that 'n' is set to 2:

i = 0, j = 0, k = 0 #will print

i = 0, j = 0, k = 1 #will print

i = 0, j = 1, k = 0 #will print

i = 0, j = 1, k = 1 #will NOT print (1 + 1 = 2)

i = 1, j = 0, k = 0 #will print

i = 1, j = 0, k = 1 #will NOT print (1 + 1 = 2)

i = 1, j = 1, k = 0 #will NOT print (1 + 1 = 2)

i = 1, j = 1, k = 1 #will print

And then, it will print the following 5 outputs:

`[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1]`

That's an extense explanation, but I'm just trying to make it as clear as possible for those who, just like me, are having a hard time figuring out what the problem wants and what the codes posted here and in the examples are really doing. Hope it helps someone.