Wouldn't it be "gutem" since it's dative neuter? It would only be "guten" if it's a weak declension, but I thought after "einem" it would be a strong declension, no?
The rule of thumb is that if the article indicates the gender and case, the adjective doesn't have to do so and so gets the generic weak ending -en.
I am not really familiar with those German learner's helpful tables, but after the "einem" has already the "m" the following adjective does never get the "m".
Look at the inflection of adjectives. We have a mixed inflection because we have an indefinite article (ein) in our case. Therefore -> guten.
It is mixed declension since an "ein" form was used. Ein/Kein/Sein/Mein/Dein and their derivatives are all mixed declension.
Under mixed declension, all dative endings (whether masc/fem/neut/plu) end in -en.
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Why is "started " more appropriate than "began", in this instance?