Oh, so it's both the luck of the draw and a sequential order? Meaning, my computer is trying to solve it's block. It might do it in 1 hour or 100 hours. Once it does, it moves on to another random block?
So an old PC joins the Bit Coin network, works on a block for 4 days and solves it, then it broadcast that out to the network where it's verified before being added to the chain? Does that mean during that 4 days, there is no way someone else is going to solve the same block elsewhere and claim ownership of it?
Your cube solving analogy was accurate.
Once someone solves 'their' block, and broadcasts it to the network, it becomes the 'next' block at the tail of the chain.
At this point everyone else gives up on the block they were working on and starts working on a new block based on the new tail.
It doesn't matter which block 'wins' as it will contain the hash of the previous tail block, which is the important bit.
Since the network as a whole tries to generate a new block every 10 minutes, 10 minutes is about how long any PC will work on any one block.