Step 1: Apply the emergency triage ladder: life and limb perfusion come before nerve, bone and skin problems. Scan the options for a vascular red flag.
Step 2: A finger turning black after trauma is the vascular emergency - it means the arterial supply is cut off and the tissue is becoming gangrenous. Delay risks permanent loss of the digit, so this patient must be escalated to the orthopaedic resident first. That makes option 1 correct.
Step 3: Compare the others. Failure to extend the arm points to a neuromuscular or tendon injury, important but reversible on a slower timescale. A 10 cm abrasion is purely superficial. An intra-articular elbow fracture is serious orthopaedically yet, lacking ischaemia, is less urgent than a perfusion-threatened finger.
\[\boxed{\text{The patient whose finger is blackening}}\]