Just curious if it is possible for a block to not be able to generate an answer (go through every possibility)? I wonder if anyone has analyzed how many possible answers there are for the various difficulties?
Also a tech question / idea for Kano... Are shares distributed sequentially or randomly to miners around the world? It seems that randomly picking shares may improve our luck (may make it worse too). I am a 30+ year web / c++ developer that has combined dedicated servers into a worldwide distributed digital signage solution. I have a concept on how to code random share distribution to deal with the trillions of shares. I am tempted to code up my own pool but have no idea where to start and have paying customers to keep happy. Kano, if this is distributed sequentially, can we chat?
If it wasn't possible to find a block, bitcoin would stop

Each individual hash is pseudo-random.
You'll not be able to find an association between two sequential hashes other than to say 'double-sha-256'
i.e. no.
Also, shares aren't distributed, work is.
The base work is the same for everyone on the pool, but the coinbase transaction is slightly different for everyone and somewhat sequential.
Each individual work item can produce more values to hash than the size of the difficulty, so you expect all work to be able to produce a block, but of course no one is able to actually exhaust a work item in 30 seconds unless they use a proxy to a VERY large number of miners (more than exist)
You wont be able to convince me of any effect due to the sequential client ids.
It effectively doesn't exist.