Ah, yes.  Thank you.  That is the facet I was missing.  So far, I understood the secret sauce of the blockchain was to require all participants to "provide proof they had worked" (a.k.a. proof-of-work) and that such work typically took about 10 minutes of CPU power to perform and that this was the way to prevent bad actors from corrupting the network.  But I had interpreted "work" as "progress" and, thus, starting over to work on a new block, or adding new transactions to a (pending) block would cause the miner to start over and, thus, "lose" any progress they had made.

I think it's less proof-of-work and more proof-of-winning-lottery-ticket.  Your analogy was helpful.

After much reading, still not clear on how a miner knows what transactions it should attempt to confirm.  I know this:

* Transactions are broadcast.
* Miners queue them in a list of "pending" transactions.
* At some point, a miner will take that list of pending transactions, create a hash, and then attempt to solve the hashing puzzle as proof-of-work.
* Once solved, the miner would broadcast what they've done and other miners validate their work and add the block of transactions to the block chain.

My questions about this are as follows:

1.  Since the hashing puzzle is based on a hash of the transactions that are proposed to be included in the next block, the miner must determine when to start that work.  The moment they start, they will, of course, be working from a block of N transactions.  How do they know when to start?  I mean, the number of transactions in each block is not fixed, right?

2.  While a miner is working on solving the hashing puzzle for the N transactions in the block they are working on, new (pending) transactions may arrive.  So now the miner has N+1 transactions.  Do they now just start over with a N+1 transaction block or does the miner ignore new transactions until (a) they solve the puzzle or (b) are notified that a new block has been added to the block chain?

3.  If new blocks added cause miners to start over, and if the number of transactions in a block is somewhat arbitrary, it seems like a miner would constantly be starting over as new transactions & blocks are broadcast, preventing them from ever getting any work done.  I guess somebody, somewhere, is getting work done but just trying to view this from a miner's perspective.