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Count number of rows with a specific MONTH in the date of a specific cell and a Boolean condition in another cell

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Let's say I have a number of dates and whether they occupy full or half a day:

   DATE  |         WHAT        | HALF?...2021-4-1 | Something Something | false2021-4-2 | Something Something | false2021-4-5 | Something Something | false2021-4-19| Something Something | true2021-5-13| Something Something | false2021-5-24| Something Something | false2021-9-13| Something Something | true...

I now want for each month the amount of half-days occupied in that list.(e.g. for April that should be 1 in the examples above, for May that should be 0)

I.e. in pseudocode, I'm looking for something like

=COUNTIF(A8:A, `MOTH of row = MONTH(E2)` AND `half of row = true`)

where E2, in this case, is e.g. January stored as a date.

And A8:A contains the dates of the above table (i.e. B8:B contains the WHAT and C8:C contains the HALF?).


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