I may not fully understand your analogy, but take issue with it inasmuch as it presents the misconception that there's "a"  block (singular) to be solved.

Without going into the math (but we could), there are numerous solutions that constitute a block; the hash computed simply needs to be less than a prescribed value based on the target and the difficultly.  Like everyone else, we're just working to find one that possesses a hash that meets the given criteria for the current round - and working to be the first pool that finds one with the current round's parameters.