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A lot would depend on where,when and the type of nuclear device that was exploded.Working backwards, for a chance of survival, those in a cave in Australia would have to have a potential maximum dosage of 250 rems.
Assuming any explosions are going to be in Europe or the USA. If the hypocentre was fairly close to the ground, the burst of a megaton bomb would rise 6,500 feet in the air.As the fireball expands and cools, afterwinds can get up to 200 mph., gaining a height of 14 miles.Depending on location of explosion, the so called nuclear winter might occur, which would reduce photosynthesis, thus effecting the life cycle of the planet.I think it is this that would effect life in Australia, as I am not so sure a cohesive radiation cloud from Europe/USA would get as far as Australia without being dissipated to levels that man could survive.Also, since Australia is an island, the danger of radionuclides migrating downwards and polluting the water course would be negligible.
Of course,all of this would change if the conflict were in Asia; when I would think the USA would be a better place to survive.
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