
dritt-
third
As an ordinal number, indicating position 3 in a sequence. The form adapts to the gender of the noun (dritter, dritte, drittes).
Sie wohnt im dritten Stock.
She lives on the third floor.
third
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third
As an ordinal number, indicating position 3 in a sequence. The form adapts to the gender of the noun (dritter, dritte, drittes).
Sie wohnt im dritten Stock.
She lives on the third floor.

as a group of three
In a group of three people.
Wir haben den Abend zu dritt in einer Bar verbracht.
The three of us spent the evening in a bar.

every third
Refers to a recurring element in every third position in a sequence.
Laut Statistik ist jeder dritte Befragte mit dem Service unzufrieden.
According to statistics, every third respondent is dissatisfied with the service.
The form 'dritt-' is only the word stem. In a sentence, the ordinal number must be declined like an adjective and takes an ending. The form adapts to the noun, e.g. 'der dritte Platz' (third place), 'die dritte Reihe' (the third row), 'das dritte Mal' (the third time).
Er hat beim Wettbewerb den dritten Platz gewonnen.
He won third place in the competition.
The form 'zu dritt' (as a group of three / the three of us) is used to describe a group of three people doing something together. It answers the question 'How many people?'. This pattern also works with other numbers: 'zu zweit' (as a pair / the two of us), 'zu viert' (as a group of four / the four of us).
Wir waren gestern zu dritt im Kino.
The three of us were at the movies yesterday.
The construction 'jeder, jede, jedes dritte ...' (every third ...) describes an element that repeats regularly in a sequence. Both 'jeder' (every) and 'dritte' (third) are adapted to the noun.
Jeder dritte Kunde erhält einen Rabatt.
Every third customer receives a discount.
three
Drei states the number of people or things and can accompany a noun. Dritt refers here to a group of three people and is used in the fixed expression zu dritt. Use drei when counting, but zu dritt when three people are acting together.

Wir arbeiten heute zu dritt an dem Projekt.
The three of us are working on the project together today.
Drei Kollegen arbeiten heute gemeinsam an dem Projekt.
Three colleagues are working on the project together today.