1230.36 – Tennis-Playing Family

A woman, her brother, her son, and her daughter (all relatives by birth) are tennis players and are obsessed with who is the best and who is the worst tennis player in the family. At the moment, the worst player's twin (one of the four players) and the best player are of the opposite sex. The worst player and the best player are the same age. Who is the worst player?

a. the woman,

b. her son,

c. her brother,

d. her daughter,

e. No solution is consistent with the given information.

Solution

Let $w$ stand for the woman, $b$ for the brother, $s$ for the son, and $d$ for the daughter. There are two possible sets of twins: $w$ and $b$ , or $s$ and $d$ . The worst and best are the same age. Possibilities for people of the same age are:

$w$ and $b$ (twins),

$s$ and $b$ (if $b$ is a much younger brother of $w$ ),

$d$ and $b$ (if $b$ is much younger than $w$ ), and

$s$ and $d$ (twins).

Now, since the worst's twin and the best are of opposite sex, and since the twins are all male-female, then worst and best are the same sex. And we know they're the same age. So the son and the brother must be the worst and the best (the only same-sex, same-age pairing). But which is which? The worst has a twin, so it must be the son.