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Count the number of occurrences in a text string

The question about [LibreOffice Calc - Number of occurrences in text string](https://stackoverflow.com/questions/63746604/libreoffice-calc-number-of-occurrences-in-text-string) from [Binz Nakama](https://stackoverflow.com/users/3483815/binz-nakama) at Stack Overflow interested me because of one of the comments posted there:
~~>OK, I think this would require a macro, AFAIK there's no single formula or combination to achieve this.~~
~~The Comment was from tohuwawohu, the user currently standing at top of the All Time list of Answerers for [libreoffice-calc], the tag applied to the Q.~~
~~The essence of the Q was:~~
>I'm looking for a formula or combination thereof that can count the number of occurrences/repetitions in a text string.
~~Examples provided in the Q were:~~
~~>if cell A1 contains "XYZXYZ", I would like to search cell A1 for "XYZ" and have "2" as a result~~
~~and, for *If B1 contains "Mary is my friend but Mary doesn't like roses"*:~~
~~>={find.repetitions}(B1;"Mary") --> 2~~
~~<sub>Aside: "Tags must have at least one tag" is odd.</sub>~~

If I have some text in a cell, how can I find the number of times another piece of text appears in it?
For example, suppose `A1` contains `fuzzy wuzzy was a bear`. `zz` occurs 2 times in this string. What formula can I put in `A2` so that it counts the occurrences of `zz` and returns 2?

excel string libreoffice-calc google-sheets openoffice-calc

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