Question

A neurosurgeon, an orthopaedist, a plastic surgeon and an ophthalmologist visited a patient after a surgery. The visit times were: Neurosurgeon 7:45, Orthopaedist 8:30, Plastic surgeon 9:15, Ophthalmologist 9:50. (Each time may be A.M. or P.M.) If the ophthalmologist generally goes for rounds before the surgeons, but not unless any other doctor does, and the neurosurgeon is not the last to go, what is the correct sequence of their visit?

• A. Orthopaedist, Neurosurgeon, Plastic surgeon, Ophthalmologist
• B. Neurosurgeon, Orthopaedist, Plastic surgeon, Ophthalmologist
• C. Orthopaedist, Ophthalmologist, Neurosurgeon, Plastic surgeon
• D. Ophthalmologist, Orthopaedist, Neurosurgeon, Plastic surgeon

Hint:

When times can be A.M. or P.M., assign A.M. to those who must be earlier and P.M. to those who must be later. Then sort chronologically to get the final order.

Answer 1

The Correct Option is C

Step 1: Decode the constraints.
- Ophthalmologist goes before the surgeons (both Neurosurgeon and Plastic surgeon).
- “But not unless any other doctor does” \(\Rightarrow\) Ophthalmologist is not first overall; at least one non-surgeon (the Orthopaedist) must have gone before.
- Neurosurgeon is not last.

Step 2: Use the A.M./P.M. freedom to satisfy the order.
Make the two surgeons visit in the P.M. so that the Ophthalmologist (non-surgeon) can be earlier than them in the A.M. while still not being first overall. A consistent assignment is:
 Orthopaedist \(8{:}30\,\text{A.M.}\), Ophthalmologist \(9{:}50\,\text{A.M.}\), Neurosurgeon \(7{:}45\,\text{P.M.}\), Plastic surgeon \(9{:}15\,\text{P.M.}\).

Step 3: Read the day’s chronological order.
Morning visits occur before evening visits:
\(8{:}30\,\text{A.M.} \to 9{:}50\,\text{A.M.} \to 7{:}45\,\text{P.M.} \to 9{:}15\,\text{P.M.}\)
\(\Rightarrow\) Orthopaedist \(\to\) Ophthalmologist \(\to\) Neurosurgeon \(\to\) Plastic surgeon.

Check constraints: Ophthalmologist is before both surgeons and is not first (Orthopaedist is first). Neurosurgeon is not last (Plastic surgeon is last). All conditions satisfied.

\[ \boxed{\text{Orthopaedist\ \rightarrow\ Ophthalmologist\ \rightarrow\ Neurosurgeon\ \rightarrow\ Plastic\ surgeon.}} \]