"How Reagan Selected Bush in 1980" joke

I heard this joke from a Czech explaining how the new leadership in
Czechoslovakia was selected. I have modified this for an American
audience.
Everyone wondered how Reagan picked Bush for VP in the first place.
Well, this is the story: Reagan knew he had to make a choice; so
he asked Nancy how he should do this. Nancy told him that he should
ask the potential candidates a riddle and see how they do. She gave
Reagan a riddle to use.
So, the next day, Reagan goes to Bush and says, "Who is it who is your
father's son, but not your brother?" Bush replies, "Golly gee, Mr. Reagan,
That's difficult. I'll need to go and think about that one for a while."
In the evening Bush returns and happily shouts, "I got it, Ron! I figured
it out! It's me! It's me!"
Reagan than goes and presents the same riddle to one of the others
(maybe Connelly, maybe Ford) and says, "Who is it who is your father's
son, but not your brother?" "That's a tough one Mr. Reagan. I'll
get back to you on that." And in the evening he returns and says,
"I couldn't figure that one out. Who is it?"
Reagan answers, "It's George Bush, but I'm not exactly sure why."
Jeff Goldberg