I have to complete the following sentence:
Wir machen die Aufgabe wider unser_ Willen.
I would write 'unsere' (accusative plural), instead in the solution they write 'unseren'?
Why? Is it an error?
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You are correct that the accusative case is needed here, however Willen is not plural, it is accusative singular of Wille:
Wir machen die Aufgabe wider unseren Willen.
Now, rules on when to use singular and when to use plural in German are not always clear-cut and they differ from English. In this case however, it is just that Wille is rarely used in plural at all. Indeed I had to look up whether it is even considered to have a plural (it is, according to DWDS).
You could probably try to argue that wider unsere Willen is also correct, but it would just sound so strange that I would have difficulty parsing it. If you said it, I might misunderstand it as wider unsere Villen. Which of course makes no sense. (That is the plural of Villa there.)