My question would be how many are actually patrolling in the same area? I assume the Russian ones are all in the relative safety of the arctic ocean.The US ones in the Pacific and Western Arctic. So the only ones that can reasonably run into each other would be the UK and French ones (possibly the Chinese and US in the pacific)wether you'd say  how many could collide would be down to how far the lengths of their patrols overlap, and so how many you'd actually have at sea at any one time.

Any idiot can face a crisis - it's day to day living that wears you out.