I recently had to re-wire a three-way switch. What I found on arrival was that when the first 3-way was down, the second 3-way would turn the fixture on and off.

When the first 3-way was up, the fixture would come on and stay on regardless of the position of the second 3-way.

There was nothing unusual about the wiring: Feed at first switch; 12/3 carrying the neutral and two travelers to the fixture; neutral ties to the fixture; 12/3 continuing travelers to the second switch and carrying switched conductor back to fixture from second switch.

Both switches had cracked casings so I replaced them both without paying attention to how they had initially been wired, but afterwards got to thinking about it:

How is it possible to wire a switch so that it will not turn off a light? I can't come up with an answer, can you?

-John