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:
- more nurses than doctors;
- more male doctors than male nurses;
- more male nurses than female nurses;
- at least one female doctor.
Give the sex and job of the speaker.
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.