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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.

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  • Consider "symbiosis" in its figurative sense of any interdependent or mutually beneficial relationship between two persons. – Graffito Apr 23 '16 at 0:37
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    A symbiotic relationship wouldn't have the light switch problem but a synergistic one could. – Mazura Apr 23 '16 at 0:43
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    Complementary – deadrat Apr 23 '16 at 0:55
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    Just synergy - no more, no less. – Drew Apr 23 '16 at 1:39
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    You clearly need a portmanteau of serendipity and synergy. How about synergipity? – Peter Shor Apr 23 '16 at 12:54
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Synergistic inadvertent catalytic relationship.

synergy, noun:

the interaction or cooperation of two or more organizations, substances, or other agents to produce a combined effect greater than the sum of their separate effects.

inadvertent, adjective:

not resulting from or achieved through deliberate planning.

catalyst, noun

a person or thing that precipitates an event.

All sources are from Google and the phrase appears verbatim in a book (note however, therein Synergistic is a column header).

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  • Supercalifragilisticexpialidocious! – Mazura Apr 23 '16 at 0:37
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You could broadly call this teamwork:

cooperative or coordinated effort on the part of a group of persons acting together as a team or in the interests of a common cause.

but a word that you used in the question (albeit misspelled) provides a more specific description of what happened: the other person's actions complemented yours:

complement:
noun
1. something that completes or makes perfect

verb (transitive)
12. to complete; form a complement to

or your actions and the other person's were complementary:

1. Forming or serving as a complement; completing
2. Offsetting mutual deficiencies or enhancing mutual strengths

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  • Yes, the complementary we should be using here is with an E. – Feralthinker Apr 24 '16 at 19:35
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"Many hands make light work." may be used to mean that doing a task is easier if more people do it together (e.g. you and your coworker) than if one person does it alone.

"Two heads are better than one." may be used to mean that, if there's a task to be done, having two people work on it together is better than one person working on it alone. (The saying has more scope -- e.g. it may be used to advise someone to get advice or an opinion from a second person.)

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  • This does not get at what the OP is asking about – Jim Jan 9 '19 at 8:14
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    In fairness, Many hands make light work is pretty funny, though. – tmgr Jan 9 '19 at 20:00
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    As a reminder, Stack Exchange answers should explain, not merely suggest. How are these expressions used, and how do they fit the need expressed in the question? Can you find examples? Without such elements, for someone learning English or simply unfamiliar with the expressions, the answer is hard to distinguish from personal opinion or conjecture. – choster Jan 9 '19 at 21:07

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