10,000 nuclear warhead detonation wouldn't affect South America? You don't really believe that, do you?

I am confidently sure of one thing and one thing alone. We lack the ability to model our planet 10 years after 10,000 nuclear detonations in a short time. Esp considering they won't be of the 14 kt Hiroshima variety.

I am reasonably sure that 100 nuclear detonations on the planet would significantly alter the world as we know it, and maybe we can model the atmospheric effects, but we cannot model all of the effects, including disease, food disruption, animal disruption, weather disruption, and most importantly social economic disruption.

Also, 100 missles seems like a good hypothetical number, which is a limited exchange by all accounts, but each missle likely has between 3-10 individual warheads as well.

Honestly, the whole damn thing is just unthinkable. It's a useless thought exercise. Humans would likely survive in some capacity no matter what short of every single region being nuked, but it wouldn't be anything close to life now. OUR world would have effectively been ended, for a new, much scarier, and horrible world.