Learn German: Wir gehen ohne den dicken Schal. - We are going without the thick scarf.

The preposition ohne (without) is a strict accusative preposition. It always forces the noun that follows it into the accusative case, regardless of context. That is why we use the accusative article den.

Why does the adjective dick get an -en ending to become dicken?

We are using the masculine noun Schal in the accusative case, which gives us the definite article den. Under the rules of adjective declension, when an adjective comes after a masculine accusative definite article (den), it must take an -en ending.

How can I tell the gender of Schal just by looking at the word den?

The accusative case only changes masculine articles (der changes to den). Feminine (die) and neuter (das) articles stay exactly the same in the accusative as they are in the nominative. Because you see den here, you know Schal has to be a masculine noun.

If I wanted to say we are going with the thick scarf, would the adjective ending change?