Troubled relationships

No reader has accepted the invitation, made last week , to propose other examples similar to the Erdös and Bacon numbers, so I will start, to see if anyone else is encouraged.

In Spain, between 20 and 30 people are struck by lightning each year, and approximately half die as a result. Let's say that if you're one of those people, your lightning number is 0; if you've touched one of those people, your NF is 1, and so on. What do you think yours might be? Although this isn't the case, numbers whose connection criterion is physical contact may be of epidemiological interest.

And speaking of physical contact, I shook hands with Queen Letizia (when she was a princess), so my manual nL is 1, and the ones who have shaken my hand are 2. What's yours?

The Spanish equivalent of Kevin Bacon could be José Luis López Vázquez, whose appearances (and not just as an actor) in films and television programs number in the hundreds. What do you think your Vázquez number could be, if by connection we mean having participated in some way in the same film or television project ?

The dubious transitivity of friendship

And isn't friendship a good connection criterion for numbers ? At first glance, it seems so, but it's misleading, because, despite the well-known—and very optimistic—claim that "the friends of my friends are my friends," in practice, this is only the case in some cases.

Friendship does not necessarily possess the transitive property, which states that if a relationship holds between the first element and the second, and also between the second and the third, then it holds between the first and the third (in mathematical terms, if a = b and b = c, a = c). How would you describe this paradoxical fact in terms of formal logic? Does it have any relation to the sorites paradox ?

Relational problems

And since we're talking about personal relationships, let's look at some relationship problems (those that have to do with kinship, not behavior, which are much more complex). We could call them brain-twisters , because they're the mental—and parental—equivalent of tongue twisters:

1. Martha is the only sister of the father of the husband of my father's only sister. What relationship does Martha's brother have with my father's sister?

2. A grandfather, two parents, an uncle, three children, a grandson, a nephew, and two brothers are sitting around a table to eat. What is the minimum number of diners?

3. Antonio is Bruno's father, Carlos is Daniel's son and Antonio's brother. Who is the father of Bruno's son's father's uncle?

4. What relationship does the uncle of my father's only sister's son have with me?

5. Three mothers and three daughters in union, how many women are there?

The real challenge is solving them mentally and without air conditioning.