drei
three
The cardinal number that follows the number 2 and comes before the number 4; the numeral 3.
Das Auto hat drei Jahre Garantie.
The car has a three-year warranty.

three
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three
The cardinal number that follows the number 2 and comes before the number 4; the numeral 3.
Das Auto hat drei Jahre Garantie.
The car has a three-year warranty.

The number 'drei' (three) is the basis for many compound words. If you see 'drei-' at the beginning of a word, it almost always refers to the number.
Ein Kind mit einem Dreirad fuhr vorbei.
A child on a tricycle rode by.
The number 'drei' (three) can also be used as a noun, for example to refer to a school grade or a house number. Then it is capitalized: 'die Drei' (the three).
Sie wohnt in der Hausnummer Drei.
She lives at house number three.
The idiom 'nicht bis drei zählen können' (to be unable to count to three) is used to express that someone is perceived as very stupid or slow-thinking. It is never meant literally.
Frag ihn nicht nach dem Weg, der kann doch nicht bis drei zählen.
Don't ask him for directions; he can't even count to three.
'Aller guten Dinge sind drei' (third time's the charm) is a well-known proverb. It is often used to encourage yourself or others when the first two attempts were unsuccessful.
Mein erster Kuchen war verbrannt, der zweite zu trocken. Aber aller guten Dinge sind drei!
My first cake was burned, the second was too dry. But third time's the charm!
third
'drei' and 'dritt' are both connected to the number 3, but they are used differently. 'drei' simply gives the quantity: 'drei Bücher' (three books), 'drei Personen' (three people), 'drei Tage' (three days). 'dritt' is not used just as freely. It appears, for example, in 'zu dritt' (in a group of three / the three of us) when three people do something together. In compounds like 'Drittplatz' (third place) or in forms like 'jedes dritte Mal' (every third time), it is about the third position in an order. Learners confuse the words because both have to do with 3. A simple rule is: for a quantity, use 'drei'; for a group of three people or a third position, you need forms with 'dritt'.

Im Garten spielen heute drei Kinder.
Three children are playing in the garden today.
Nach der Arbeit sind wir zu dritt nach Hause gefahren.
After work, the three of us went home together.