I have found when setting up v-brakes that adjusting the brake cable to ensure the brake pads do not touch the rims is a bit of trial and error affair, and the instructions with a Shimano brake set I bought say the brake pads should be a millimetre away from the rim on each side. (The docs actually say a combined total of 2mm)
After some frustating unsuccessful attempts I came to this strategy which seems logical to me but may not be so in practice.
Clamp the brake pads firmly against the rim with the cable pulled as tautly as possible and tighten the pinch bolt. If done right it should be impossible to pull out the noodle from its holder and brake pads should keep the wheel locked
Release the cable by the minimum length plus a millimetre or so needed to enable the noodle to come out of the holder, then tighten the pinch bolt. It may not be actually necessary to tighten the pinch bolt at stage 1 if you have an eye for the required length. Just pull it taut and release it accordingly.
I also follow the Park Tools advice on loosening the barrel adjuster to the last two turns to use those to loosen the brakes at the end of the process if they wind up too tight without having to adjust the cable again at the pinch bolt.
I estimate that if there is no slack in the cable, the gap between the pads and the rim should be somewhere near the combined total of 2mm required, but this assumes that the length of metal at the end of the noodle holder must be the same on all noodles, and all brake levers pull an equal length of cable dependent on the degree of rotation.
So, is the amount of metal that sticks out of the noodle holder a set standard on noodles or does it differ between manufacturers and models?