Sorry, but duo's version is the right one ;-) When inflecting adjectives, 'manche' qualifies as an article (German nomenclature: Indefinitpronomen) ;-) http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html (see common problem 2). This one was a bit unfair, I agree ;-)
thanks for your reply wataya I read the page you linked but I still do not get it. If manche qualifies as an article the adjective that follows is supposed to follow the weak inflection and that means its ending should be -en. If I am correct there is only one possibility for an accusative plural adjective to have the -e ending: that is the strong inflection. Where is my mistake?
I just got really confused. In my first post I agreed with you that it should be "schwarzen", but I listed reasons why it should in fact be "schwarze". -1 point for Hohenems.
Then after wataya pointed out that manche is a "der" word and that Duo's "schwarze" was right, I agreed. -2 points for Hohenems.
Now that you've re-asked the question, I'm agreeing with you again. Manche = der word, accusative case, plural noun = -en ending.
I wonder if I'll get a point back or if wataya will come and squash it and I'll be at -3 points.
OK, christian just answered my question on my stream. As he'd say 'hat manche schwarzen Punkte' and as he doesn't have any objections against 'hat manche schwarze Punkte', I think we should settle it according to what canoo.net says which looks very reasonable
in singular: use weak adjective inflection with the inflected 'manch...' forms
in plural: both weak and strong inflection are fine
adjectives after the uninflected form of 'manch' are always inflected according to strong declension
So, you can stick to the rules you learned and I can stick to my Sprachgefühl. Happy outcome ;-)
These are very good and valid points. The matter is even more complicated than I thought and wrote above. As I said, German declension is an abyss: http://www.canoo.net/services/OnlineGrammar/Wort/Adjektiv/Deklinationstyp/Schwankend.html
I knocked on christian's door and I hope he'll contribute his opinion. It may well be that both 'schwarze' and 'schwarzen' are ok to use. My personal Sprachgefühl still tends strongly towards 'schwarze' but this might be a regional thing.
@Hohenems (and max): very clear and thoughtful observations. That's a +5!
Waiting for further input from other native speakers...
And deeper I will go. It is even listed in one of my go to sources (the same page I linked up ^ there) as a "der word".