On a violin, the lowest note is the open string 'G' below 'Middle C'. It is relatively easy to play the 'G' that is 3 octaves higher but a good violinist can play hundreds of notes much higher than that.
Some string instruments, such as the guitar or mandolin, have frets going across the fingerboard which allow only certain predefined notes to be played.
There are no frets going across the fingerboard of the violin, so - because each finger's position can be varied very finely - it is impossible to say exactly how many different notes can be played by a skilled violinist.
The first answer shown above could perhaps be trying to describe the notes played in what is called the "First Position" but is incomplete because it fails to mention:
- that you must learn how to play semitones (half notes) accurately, so that you can play tunes in both major and minor modes of the five main key signatures (A, B, C, D, E, F, G) and their flat and sharp key signature variants (A flat, B flat, C sharp, E flat, F sharp);
- that, in addition to playing normally, by using full finger pressure on a string, you must learn how to produce even higher notes by using the "harmonics" made by allowing a finger to touch lightly against a string in a controlled manner;
- that there are several higher positions - above the 1st position - which you must learn to be able to play even a small amount of the vast range of music that has been written for the violin.
After you have learnt how to play in 1st position, the next one to learn is the 3rd position, followed by the 2nd position and then the 4th.
There are several more positions after those first four, but you would have to achieve a very high standard of playing to be able use them...