If you read James Watson's The Double Helix, that's exactly how they finally worked out the molecular structure of DNA. Lots of other people were trying it out conceptually, on paper, and in their heads... Watson and Crick had models made of the sub-structures, and they put them together in various ways until they figured out a way that worked.
Why hasn’t a computer already figured out the different possibilities? I ask this question out of complete ignorance on the subject.
Not quite, a lady had made photographs (x-ray photographs) of DNA and this prompted Watson and Crick to ‘discover’ the ladder shape of the double helix. She, BTW, was not credited in their accolades.