Write a short story (approx. 1000 words) that utilizes a non-linear narrative structure. The plot should revolve around a detective solving a cold case. However, the story must be told out of chronological order, jumping between the present investigation, the day of the crime, and the detective's childhood memories. Ensure that thematic cohesion binds these disparate timeframes together, revealing a crucial clue only through the juxtaposition of these separate timelines.