I get the feeling that German wanted to be like Greek, with four cases, two numbers, and three genders for the nouns. The problem is there weren’t enough German endings to go around; so the language made do with what it had. The 24 functions of the definite article are supplied by the 6 forms: der, die, das, dem, den, and des. Noun endings are basically limited to –(e)s, e, er, and (e)n. Review the chart of the definite article.
This means that, for example, you can’t really identify the Gender, Number, and Case of the form der or den, for example, by itself. Once you know the Gender of the noun it precedes, you can eliminate possible choices from the other Genders. That is why it is essential to memorize the Gender of the noun (or better, just learn the definite article with it) when learning vocabulary.
Review again the sentences below, and notice how the Gender of the noun, and whether the noun is singular or plural, determines the case of the article: