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There isn't only this askbot site. There is also a well structured forum on open office suites (including LibO) where you can find well proven solutions without searching with the finger in the haystack.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Sectionj "C." and the example document attached there apply to your question.

There isn't only this askbot site. There is also a well structured forum on open office suites (including LibO) where you can find well proven solutions without searching with the finger in the haystack.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Sectionj "C." Section "C." "E." (Sorry!) and the example document attached there apply to your question.

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There isn't only Besides this askbot site. There site, there is also a well structured forum on open office suites suites (including LibO) where you can find well proven solutions without searching with the finger in the haystack. solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.

Besides this askbot site, there is also a forum on open office suites (including LibO) where you can find solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.question.

(Editing:)
Though the OQ didn't answer my questions I prepared this attached demo.
You may take from it what seems useful to you.

Besides this askbot site, there is also a forum on open office suites (including LibO) where you can find solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.

(Editing:)
Though the OQ didn't answer my questions I prepared this attached demo.
You may take from it what seems useful to you.

(Edit2 regarding the recent explanations by the OQ:)
To create a new partition-into-pairs is simple using the means I already demonstrated, but I would judge it next to impossible (probable solutions at least very inefficient) to definitely avoid any reoccurring pair by Calc means. If a respective guarantee is needed I would resort to user code. (Also not exactly simple. These comments are based on estimations, of course.)

Besides this askbot site, there is also a forum on open office suites (including LibO) where you can find solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.

(Editing:)
Though the OQ didn't answer my questions I prepared this attached demo.
You may take from it what seems useful to you.

(Edit2 regarding the recent explanations by the OQ:)
To create a new partition-into-pairs is simple using the means I already demonstrated, but I would judge it next to impossible (probable solutions at least very inefficient) to definitely avoid any reoccurring pair by Calc means. If a respective guarantee is needed I would resort to user code. (Also not exactly simple. These comments are based on estimations, of course.)

course.)

(Edit2:)
The proper way is to create one maximal table of partitions into pairs for the numbers from 1 through N (20 in your case) by deterministic means, and, if randomization is wanted, to do it for the complete campaign by randomizing the order of the names (I showed that) and the order in whitch the partitions are chosen. In addition you may randomly decide in which order any pair is "published".
For your 20 students you get exactly 100 different pairs (order ignored) and these can be divided in exactly 10 pairings without the repetition of any single pair. It's the same as if you have to create a raw playing schedule (one round only) for a league of 20.

Besides this askbot site, there is also a forum on open office suites (including LibO) where you can find solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.

(Editing:)
Though the OQ didn't answer my questions I prepared this attached demo.
You may take from it what seems useful to you.

(Edit2 regarding the recent explanations by the OQ:)
To create a new partition-into-pairs is simple using the means I already demonstrated, but I would judge it next to impossible (probable solutions at least very inefficient) to definitely avoid any reoccurring pair by Calc means. If a respective guarantee is needed I would resort to user code. (Also not exactly simple. These comments are based on estimations, of course.)

(Edit2:)
The proper way is to create one maximal table of partitions into pairs for the numbers from 1 through N (20 in your case) by deterministic means, and, if randomization is wanted, to do it for the complete campaign by randomizing the order of the names (I showed that) and the order in whitch the partitions are chosen. In addition you may randomly decide in which order any pair is "published".
For your 20 students you get exactly 100 different pairs (order ignored) and these can be divided in exactly 10 pairings without the repetition of any single pair. It's the same as if you have to create a raw playing schedule (one round only) for a league of 20.
(deleted; was not good)

Besides this askbot site, there is also a forum on open office suites (including LibO) where you can find solutions.

In your case: https://forum.openoffice.org/en/forum/viewtopic.php?t=58665
Section "C." "E." (Sorry!) and the example document attached there apply to your question.

(Editing:)
Though the OQ didn't answer my questions I prepared this attached demo.
You may take from it what seems useful to you.

(Edit2 regarding the recent explanations by the OQ:)
To create a new partition-into-pairs is simple using the means I already demonstrated, but I would judge it next to impossible (probable solutions at least very inefficient) to definitely avoid any reoccurring pair by Calc means. If a respective guarantee is needed I would resort to user code. (Also not exactly simple. These comments are based on estimations, of course.)

(Edit2:)
(deleted; was not good)

good)
Now hopefully better:
What you actually need has little do do with randomizing. Depending on the preferred words it is nown as a chapter of mathematical graph-theory, or more pragmatically - often needed - the task to schedule (sine-die) the first set of matchdays for a 20-league. In your case the participants are just not expected to fight one another.

Theory: http://www.mathaware.org/mam/2010/essays/FroncekTournament.pdf
Spreadsheets for the task: http://www.excelformeln.de/bilder/Liga-Spielplan.zip
(German; no understanding of the language needed. Simply replace the names.)
(Author's page in that site: http://www.excelformeln.de/uberuns.html?umenuzahl=14&autor=1)

If randomization shall be included you may first of all randomize the order of names (and leave it at that then) or randomize the order of the pairings you want to apply them in (or both).

The linked sheet is in .xls and contains relics of VBA though there is no active code at all. I made an .ods of it without the macro modules ("hard work") and it still did its duty. Of cours you may simply reject permission for macros.