Hospital Staff (Doctors, Nurses)

A staff member of a small hospital said, “The hospital staff consists of 16 doctors and nurses, including me. The following facts apply to the staff members; whether you include me or not does not make any difference.”

The staff consists of:

  1. more nurses than doctors;
  2. more male doctors than male nurses;
  3. more male nurses than female nurses;
  4. at least one female doctor.

Give the sex and job of the speaker.

Show/Hide Solution

If you try to sprinkle numbers totalling 16 into a grid like this one, you’ll soon see that it’s not so easy.

Back off from the random approach, and observe that mn + fn ≥ 9, with mn > fn and md > mn. So try this:

These numbers work, leaving 1 for fd.

Next try 6 male nurses. Then you get this,

and fd is 0 (can’t have that).

So this seems to be the only possibility.

But who’s talking? It has to be a person such that the four conditions are still met if the number drops by 1. So the only possibility is … a female nurse.

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