
zu dritt
in a group of three
Describes that a group consists of three people or that an action is carried out jointly by three people.
Wir waren gestern zu dritt im Kino.
There were three of us at the movies yesterday.
third
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in a group of three
Describes that a group consists of three people or that an action is carried out jointly by three people.
Wir waren gestern zu dritt im Kino.
There were three of us at the movies yesterday.

third-
As part of compound words, used to indicate the position 'in third place' in an order.
Frankfurt hat den drittgrößten Flughafen Europas.
Frankfurt has the third-largest airport in Europe.

every third
Refers to an element that always stands in the third position in a regular sequence.
Jeder dritte Befragte war mit dem Service unzufrieden.
Every third respondent was dissatisfied with the service.
The form 'zu dritt' (as three / in a group of three) is part of a series ('allein' (alone), 'zu zweit' (as two), 'zu dritt' (as three), 'zu viert' (as four), etc.) that indicates how many people a group consists of. The expression is invariable and is used like an adverb.
Wir sind zu dritt in den Urlaub gefahren.
The three of us went on vacation together.
As the first part of a compound word, 'dritt-' means 'in third place'. In these words, 'dritt-' remains unchanged, while the second part, usually a superlative, is declined.
Er hat die drittbeste Zeit im Wettbewerb erreicht.
He achieved the third-best time in the competition.
In the construction 'jeder/jede/jedes dritte' (every third), 'dritte' is declined like a normal adjective. This expression selects an element from a regular sequence.
Jedes dritte Auto auf dem Parkplatz war rot.
Every third car in the parking lot was red.
third
Dritt and Drittel both relate to the number three, but they do not mean the same thing. Zu dritt describes three people doing something together, while ein Drittel means one of three equal parts. Use dritt for a group of people and Drittel for a portion.

Wir gingen zu dritt zum Markt und kauften frisches Gemüse.
The three of us went to the market and bought fresh vegetables.
Jede der drei Familien bekam ein Drittel des Kuchens.
Each of the three families received a third of the cake.