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Since users repeatedly ask us, why this word is neuter, I decided to write a very detailled explanation. Here it is:
I know that this word is a really tough one to learn in the very first skill, but we cannot change the system (yet). German grammar has a lot of idiosyncrasies and your assumption that "eine" goes with a feminine noun is absolutely correct.
It is "das Mädchen", neuter and there is a logic why, though. In German, every noun that can be diminished (ladies and gentlemen, let me introduce: The diminutives) and is formed of its stem and the suffixes -lein or chen is neuter. Now please imagine that a girl is a little woman, OK? The word "Mädchen" stems from the old German word Maid (Maid = unmarried woman) or from the old German word Magd (Magd = farm girl or chambermaid). A young Maid or Magd was called Maidchen or Magdchen and as the language developped, these forms turned into the word Mädchen. Since a Mädchen is logically younger than a woman, you have to add the suffix -chen and this is the reason why we say das Mädchen. To sum it up, the grammatical gender is thus neuter, whereas the girl is still a biologically feminine being ;-)
For those of you who want to have another explanation of said suffixes: You can add them to a lot of different nouns (but not to every noun!). If the stem of this noun consists an a, the a of the diminished form converts into the umlaut ä. The same happens for o - ö and u - ü. Please compare these examples and notice how the grammatical gender changes:
- das Brot (the bread) - das Brötchen (the bread roll)
- das Schiff (the ship) - das Schiffchen (the boat, the little ship; no a/o/u here)
- der Turm (the tower) - das Türmchen (the turret, the little tower)
- die Tafel (the board/panel) - das Täfelchen (the small board, the small panel).
Please notice that this refers to the singular only! The plural of a noun always goes with "die". Compare the singular of the diminished form with its plural form:
- das Brötchen (only one) - die Brötchen (more than one ;-) )
- das Schiffchen (only one) - die Schiffchen (more than one) a.s.o.
Hope this helps =)
Ps.: Since this discussion has become very cluttered, I deleted a lot of the comments because every question is now covered from all the remaining posts here. If you have further questions that have not been asked yet, don't hesitate to ask them. Thanks!