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I've got a sheet with account numbers in column Q. If the account number is 9 I want it to say "Yay", if not 9, "Boo".

=ARRAYFORMULA(If(Q3=9,"Yay","Boo")

This simple formula doesn't fill down.

Columns E & L on the same sheet have arrayformulas that fill down the column, but Column R won't work. I've tried inserting in a new column and typing the formula fresh in cell R3 and still doesn't fill down.

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Your formula is filling down, but you are asking it to fill down one row only. To get 100 results, specify 100 rows in the parameter range, like this:

=arrayformula( if(Q3:Q102 = 9, "Yay", "Boo") )

To fill down all the way to the bottom of the sheet, use an open-ended reference, like this:

=arrayformula( ifs(Q3:Q = 9, "Yay", not(isblank(Q3:Q)), "Boo", true, iferror(1/0) ) )

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