Each solution to the problem we were trying to solve would have independently failed. We were each trying many different solutions at the same time. We each happened to try a solution that worked, but only because the other had tried a complimentary solution.
Is there a word, phrase, idiom, or analogy that describes such a solution?
An example: It's like if we had a whole bunch of light switches and were flipping each of them on and off to see if it controlled the light we were trying to turn on. Unbeknownst to us, the light needed two specific switches to be turned on. Had we been trying independently, we'd have flipped one on, seen no reaction, then flipped it off. However, we happened to each flip one of the two correct switches at the same time, causing the light to turn on. We then each thought we had found the correct one switch, but in further experimentation we realized that the light had needed both of us to switch on the two switches at the same time.
It was an interesting (and probably very lucky) event. I've been trying to come up with a word or phrase to describe it, but I am only getting generalizations like it was 'serendipitous' or it was like we had built two halves of a bridge.