One of Mr. X, his wife, their son and Mr. X's mother is an Engineer and another is a Doctor.
1. If the Doctor is a male, then the Engineer is a male.
2. If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.
3. If the Engineer is a female, then she and the Doctor are blood relatives.
Can you tell who is the Doctor and the Engineer?

Of help here will be the 3 statements in their contrapositive form:

1CP: If the Engineer is female (not male), then the Doctor is female (not male).

2CP: If the Engineer and the Doctor are blood relatives, then the Doctor is younger than the Engineer.

3CP: If the Engineer and the Doctor are not blood relatives, then the Engineer is male (not female).

From 3, if the Engineer is female, then she and the Doctor are blood relatives. From 1CP, if the Engineer is female, then the Doctor is female. Here we have a contradiction since the two women in the problem are not blood-related.

Thus: The Engineer is male.

A. Suppose now that the doctor is also male.

If follows that the two people we are looking for are the father and his son, who are blood related. It follows from 2CP that the Doctor is younger, and therefore the Doctor is the son and the Engineer is Mr. X. This solution does not violate any one of statements 1-3 nor their contrapositives.

B. Suppose instead that the Doctor is female.

If the male Engineer is the son who is blood related to everyone in the problem, then the Engineer and the Doctor are blood related, and by 2CP, the Doctor is younger than the Engineer, a contradiction since the son is the youngest person in the problem. Therefore the male Engineer would have to be Mr. X.

If the female Doctor is Mr X's mother, then they are blood related, and so by 2CP, the Doctor is younger than the Engineer. This is a contradiction since Mr. X's mother can not be younger than Mr. X. Therefore the female Doctor would have to be Mr X's wife.

This means that the male Engineer Mr. X and the female Doctor (his wife) are not blood related. This arrangement also does not violate any one of statements 1-3 nor their contrapositives.

So: 2 possible solutions to the puzzle.

Posted by Mike C on 2007-08-30 14:57:41