"Nein, ein anderes."
Nein. Das ist nicht gut. Niemand sagt "No, one different". Und es ist nicht "No, a different", es ist "No, a different ONE". Oder, ich denke mehr genauer "No, another"?
You have to keep in mind though, that not all languages follow English rules in grammar or syntax. "No, a different" is correct in a LITERAL translation, but literal translations can sometimes be of little use when you're trying to desipher what the speaker/text is really trying to put across. Just translate all the previous german sentences in this course word for word and you'll realise most don't make sense when translated literally.
This can't be stressed enough. It should be obvious by now that you simply can't translate word-for-word
That's not correct English. You can't translate these examples word for word all the time.
It is correct English, actually. An other isn't contracted but it's often a more precise or formal way of distinguishing difference than saying "another": instead of gesturing sequentially, it shows genuine "otherness." Theoretical discussions often refer to "an other" for that reason.
Why no "No, other one?" If it's not correct translation how would you translate this sentence to German.