The Gerundivum in German: zu + Partizip I as an Attribute (C1)

The gerundivum is a noun attribute built from zu + Partizip I (present participle) + adjective ending: das zu lösende Problem = "the problem that must/can be solved". Although it is formed from the present participle, its meaning is passive and expresses necessity or possibility — it is equivalent to a relative clause with werden müssen/können: das Problem, das gelöst werden muss/kann.

Build it in three steps: take the infinitive (lösen), form the present participle (lösend), put zu in front (zu lösend), and add the normal attributive adjective ending that the article and case require (das zu lösende Problem, die zu lösenden Probleme). The participle sits between the article and the noun, just like any other adjective.

Crucially, do not confuse the gerundivum with the plain Partizip-I attribute (without zu), which has an active meaning: das lösende Verfahren would mean "the solving procedure" (something that is solving), whereas das zu lösende Problem means "the problem to be solved" (something that gets solved). The little word zu flips the voice from active to passive. The gerundivum is formal and chiefly written (reports, law, academic and technical texts) and is a hallmark of C1-level German.