One of the four people - Mr. Brown, his wife Monika, their son Mandy and their daughter Cindy - is a singer and another is a dancer.

1. If the singer and the dancer are the same sex, then the dancer is older than the singer.
2. If neither the singer nor the dancer is the parent of the other, then the singer is older than the dancer.
3. If the singer is a man, then the singer and the dancer are the same age.
4. If the singer and the dancer are of opposite sex then the man is older than the woman.

Whose occupation can you deduce with absolute certainty?

Suppose the singer is older than the dancer. Then, by 1, the singer and the dancer are of opposite sexes. By 4, the man is older than the woman. Therefore, the singer is a man and the dancer is a woman. Then, by 3, they are the same age, which contradicts what we supposed. Therefore, the singer is not older than the dancer. By 2, one of them is the parent of the other. Since the singer is not older than the dancer, the dancer is the parent of the singer. Then, they are not the same age, so by 2, the singer is a woman. Therefore, Cindy is the singer.

Posted by Math Man on 2013-06-22 09:00:34