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I have trouble with displaying one of three questions, I already followed guidelines on randomization and everything looks neat but the problem still occurs. 

You should tell us what the problem is. You just say there is a problem, but what is it? What did you try? What was the outcome?

The LSS file helps, but can only tell so much.

Will have a look at it later.

Very difficult to help you when you provide a questionnaire in a language that most of us don't speak and also do not delete the unnecessary parts.

I assume the questions you want to show 1 out of 3 randomly are the ones in the last question group? "Przykładowa sytuacja nr.1"?

So you created a question called "Randgroup". I assume that is where things should happen?

But it is at the end of this group, it is empty and it is referred to in questions that are before it, like in this relevance equation:

So you only want to show this question if Randgroup==1. But Randgroup contains nothing in your example. So it can never be 1.

Also, Q002 is a text question, so the answers are stored as a text, but you want to compare it as a number. That might be another issue.

So there are a couple of issues going on.

Maybe you can create a dummy survey in English with only the questions relevant for this problem, so we can actually understand what you are trying to do? I find it very hard to understand your survey.

Here is the dummy survey, containing only the questions related to the problem. I changed the text question to a regular one hoping this might solve part of the issue. Instead of showing one of three questions from randomised pool, the survey shows only the name of question group and no questions at all. What I am trying to achieve here is the survey showing randomly one of three questions in the question group, possibly with them being shown in proportions 1:1:1.

Thank you kindly for your help.

Your "equation" is wrong. 

An equation is surrounded by curly brackets -> {rand(1,3)}
Better you use the construct that holch showed {if(is_empty(RANDGROUP),rand(1,3),RANDGROUP)}

And instead of using the conditon agreement.NAOK == "Y" and !is_empty(age.NAOK) && age.NAOK >= 18 in all following groups
(where you do not need !is_empty(age.NAOK) - if the age is >17 it is obviously not empty)
you'd better use a quota

Joffm
BTW: In my opinion it's better to place the equation in the question text insted in the setting "equation"

I have applied the changes, the problem persists. Not sure why, maybe I misunderstood the instructions. Whenever I preview "Randomised question" question group it displays only "Randomised question" group name, nothing else, when I preview the whole survey it just skips "Randomised question group".

Thanks in advance.

If you applied the changes and still get issues,
show what you did.
less export 

Joffm 

BTW:
I do not see any issue.

Sorry, I was sure the file was attached. 

Sorry, but why didn't you import and study the sample I sent?

In your survey the equation vanished; insted there is a question of "short text" with a condition "{if(is_empty...)}.
How do you expect this to work?.
And you hide this question.
While testing you shouldn't hide a question.

Joffm