What is the word for a 'hint' that might help give the solution at the end of movies?

Solution 1:

I think this is typically called a "foreshadowing" element or maybe "planting and payoff." It's a staple of James Bond movies -- and it's everywhere in the Back to the Future trilogy.

Solution 2:

"Chekhov's Gun" After Anton Chekhov, the playwright. The idea is usually paraphrased as "If you show a gun in the first act, it must be fired by the last."

"Remove everything that has no relevance to the story. If you say in the first chapter that there is a rifle hanging on the wall, in the second or third chapter it absolutely must go off. If it's not going to be fired, it shouldn't be hanging there." — Anton Chekhov -

Solution 3:

If you're trying to convey that the early image of the pyramid could be used (by attentive audiences) to solve the mystery present in the film, you might call it an easter egg, which Urban Dictionary defines as

"A hidden item placed in a movie, television show, or otherwise visual media for close watchers"

As an example of an easter egg, consider a scene from the movie Fight Club [warning! spoilers]. In the scene, the protagonist receives a call on a payphone, despite the fact that a sign on the payphone reads "No incoming calls allowed". This clues the audience in that the protagonist is hallucinating, but it is very unlikely to be noticed.

If the early image doesn't help you solve the mystery, you might just call it foreshadowing (in some weak sense). If the pyramidal imagery shows up throughout the work, you might try motif.