How do I complete the puzzle with the Flare Gun in Into The Abyss?

In Into The Abyss the cart comes to a stop outside a closed door where you will be instructed to use the Flare Gun on the puzzle piece to open it. A tutorial hint will drop down to show this.

 

When the door opens, the cart moves into the grander puzzle room, where you have to find shoot 5 of the puzzle pieces to open the door ahead. Each shot piece will illuminate a torch above the door

 

 

If you do not resolve this in 3 loops, part of the roof will collapse and the cart will crash, causing your imminent death. 

If you do solve the puzzle, the door will open and they will progress to the next area.