The plumber said, "Re-pipe the house."
What does re-piping mean? Finding where, on a 111 year old house, all the cold water pipes are.
What does that mean? Ripping out the walls and ceiling in a very unappealing bathroom. There are separate pipes to every fixture in our house.
Our mission, should we choose to accept it, is to rip out until we find where in the walls the pipes are that feed: our bathroom sink, our kitchen faucet, our toilet (found), our bathtub, and our washer. Another Saturday projecting on something we didn't plan to do. I guess we have found our winter remodel project after all.
The good news? We have hot water (go figure) so that dishes can be done. Jackson learned a very important bit of information, you can flush a toilet if you fill up a bucket and pour it down. You can also wash white clothes in hot water. The unappealing bathroom will be, in the end, remodeled.
The lesson; when you hear water running at odd times you can ignore it and hope it goes away (I tried that for a few days), or you can investigate to find you have a broken cold water pipe under the concrete in the basement resulting in hearing the plumber say, "Re-pipe."
Photos of the progress may be posted.