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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.