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[So much for freedom of speech! I guess this comes under freedom of listening or not. . .]
I found it is much easier to predict the results given the schematic instead of the other way around, but I can't resist a good puzzle.
An "impossible outcome" means that we are assuming something that is not true.
What's good about these is that we will probably learn something new. Plus, nobody else wants these budget-busters.
To find out what it is I'd say check #1 switch with an ohmmeter. If it checks good something has changed inside the walls and that's a separate troubleshooting procedure involving a voltmeter and incand. bulbs.
There are many different wiring diagrams for this, but I can only find two schematics. In any case it's a source in series with a load in series with an SPST switch made up of two 3-way and zero or more 4-way switches.