An alternative answer that does away with "mixed declension" and reference to definite or indefinite articles. This answer deals with attributive adjectives, i.e. those modifying a noun, since predicative and adverbial adjectives bear no endings.
Das hast du aber schön gesagt. (adverbial adjective)
Wir finden den Vorschlag nicht gut. (predicative adjective)
Basic Rules
Adjectives have two sets of endings: strong and weak.
1. The adjective bears a strong ending when it is not preceded by a determiner, or when the determiner preceding it bears no ending. Note hat prenominal genitives behave like a determiner without an ending.
Ø kühles Bier, ein-Ø kühles Bier
Ø schöne Blumen, welch-Ø schöne Blumen
mit Ø neuem Design, mit manch-Ø neuem Service
Merkels Ø jüngster Vorschlag
2. The adjective bears a weak ending when it is preceded by a determiner bearing an ending.
dieses kühle Bier
welche schönen Blumen
mit manchem neuen Service
der jüngste Vorschlag Merkels
3. The strong endings of adjectives are identical to the endings of determiners (pronominale Flexion: dies-er, jen-es, jed-e, welch-e, ...), with the exception of the genitive singular masculine and neuter, where the adjective has -en instead of -es.
jener Vorschlag = guter Vorschlag
welches Brot = frisches Brot
aufgrund dieses Problems ≠ aufgrund defekten Materials
4. The weak ending is -e in the nominative singular only and -en otherwise. (Note that, outside of the masculine singular, nominative and accusative are always identical, so that the accusative singular neuter and feminine also has -e).
dieser/dieses/diese kluge Mann/Kind/Frau
diesen klugen Mann
diese klugen Menschen
mit diesem/diesem/dieser/diesen klugen Mann/Kind/Frau/Menschen
5. Multiple adjectives modifying the same noun bear the same ending.
das umfangreiche technische Equipment
umfangreiches technisches Equipment
but: eine gut gewählte Analogie (gut modifies gewählte, not Analogie)
Note that rules 1 and 2 reference inflected word forms and not words (lexemes). In German, certain determiners (such as the the indefinite article ein, the negative determiner kein and the possessive determiners mein, dein, ...) have no ending in the nominative singular masculine and neuter. When they have no ending, they fall under rule 1 (ein kühles Bier); when they have one, they fall under rule 2 (mit einem kühlen Bier).
Adjective or Determiner?
Beware of homonyms such as the following.
mit einem einzigen Punkt (indefinite article)
mit dem einen Punkt (numeral adjective)
beide neuen Modelle (determiner, triggers weak inflection)
die beiden neuen Modelle (adjective, bears weak inflection)
Note that viel-, ander- are adjectives.
viele kluge Vorschläge, ein anderer Betroffener (strong by rule 1)
die vielen klugen Vorschläge, der andere Betroffene (weak by rule 2)
Deviations from Basic Rules
In the dative singular masculine and neuter, -m is often replaced by -n on adjectives following an adjective ending in -m, counter to rule 5.
mit umfangreichem technischen Equipment
A violation of the basic rules regularly occurs in appositions with wir.
wir Deutschen, wir beiden (weak, unexpected)
wir Deutsche, wir beide (strong, as expected)
The words folgend- and sämtlich- sometimes show unexpected strong inflection.
folgendes gesellschaftliche Problem (determiner triggering weak inflection)
das folgende gesellschaftliche Problem (adjective)
folgendes großes Problem (unexpected strong inflection; expected große)
sämtliche anwesende Bürger (unexpected strong inflection; expected anwesenden)
In certain fixed expressions or old-fashioned speech, endings may be dropped.
auf gut Glück
Ein garstig Lied! Pfui! ein politisch Lied! Ein leidig Lied! (Goethe)
Declension Table
|
masc. |
neut. |
fem. |
pl. |
n. |
-er -e |
-es -e |
-e -e |
-e -en |
a. |
-en -en |
-es -e |
-e -e |
-e -en |
d. |
-em -en |
-em -en |
-er -en |
-en -en |
g. |
-en -en |
-en -en |
-er -en |
-er -en |
Left forms are strong, right forms are weak.
Observe how the strong forms are identical to those of determiners such as dies-er, with the exception of the genitive singular masculine and neuter.
Observe how the weak forms have -e in the nominative singular (and accusative singular neuter and feminine) and -en elsewhere.
Terminology
The term determiner is used instead of article to emphasize that these rules not only apply to definite and indefinite articles (der, ein, ...), but also words such as alle, jeder, welchen, keinem, ihres, ...
The terms strong and weak have been used as far back as Jacob Grimm's Deutsche Grammatik (1822) (source).