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?

A statement of the form "if A, then B" can be ignored if A is not true.

If the doctor is a female younger than the engineer, and the engineer is a male, then all three statements can be ignored.
This is possible only if Mr. X is older than his wife, and he is the engineer while she is the doctor.

If the first "if" statement is true, and the other two are still false, we have another valid solution. This happens when the doctor and engineer are both males, and the engineer is older than the doctor.
There are only two men in the problem, so this occurs when Mr. X is the engineer and his son is the doctor.

Suppose only the second "if" statement is true. That means the doctor is a female, the engineer is a male that is younger than the doctor, and they are not blood relatives.
Either of the men (Mr. X and his son) could be younger than either of the women, so we just need to find a man and woman that aren't blood relatives. The son is a blood relative to each of the other three, and Mr. X is a blood relative to his mother and his son.
Therefore, this only occurs when Mr. X is the engineer, his wife is the doctor, and she is older than him.

If only the third "if" statement is true, then the doctor and engineer are both female, the engineer is older than the doctor, and they are blood relatives. Since the only two women in the problem are not blood relatives, this will never happen.

If both of the first two "if" statements are true, then both the engineer and the doctor are male, but they are not blood relatives; this is not possible.

Similarly, if the second and third "if" statements are both true, they are blood relatives and they are not blood relatives; we have an obvious contradiction.

Finally, if the first statement is true, both are males, and the third will never be true.

That is the entire realm of possiblity, and there are three combinations of the parity of the statements that yield a valid conclusion. Two of these are equivalent, except for whether Mr. X or his wife is older, so there are two disctinct possiblities for who are the doctor and the engineer.

• Mr. X is the engineer and his wife is the doctor.

  or
  



• Mr. X is the engineer and his son is the doctor.

Posted by DJ on 2003-08-25 10:44:55