# Attendance at a dinner party

In the late 1400's, a Count, who is hosting a dinner party, receives a message from his steward. The note lists that the following relatives of the Count will be attending the party:

• The father's brother-in-law
• The brother's father-in-law
• The father-in-law's brother
• The brother-in-law's father

The Count immediately assumes that there will be four guests. However, the steward's message makes him seem less sure.

What is the least number of guests that the Count can expect?

• For this problem, are you allowing either remarrying or incest? Those could be used to reduce the number. – Lacklub Mar 4 '16 at 13:56
• I want to add an answer as "No Party" and explanation as "Consequences" :D – manshu Mar 4 '16 at 14:08

It's:

They could all be the same person in a totally respectable manner.

Because:

The father's brother-in-law isn't necessary his uncle. The father could have remarried.
The brother's father-in-law could be that person if the father's new wife is his brother's wife's mother.
The father-in-law's brother is also the same person if he's his wife's father's brother.
The brother-in-law's father can still be the same person if his wife's her brother's mother remarried her ex's brother.

• This answer is correct, as it does not involve marrying more than one person, as does the other answer. Good job! – Quiquȅ Mar 4 '16 at 15:33
• This could be simplified if you remember that brother-in-law can also mean your sister's husband (or brother's husband if you like) not just your spouse's brother. – Dan Jenks Mar 4 '16 at 16:27

Zero other than himself.

The count is married to his aunt, thus his father's brother-in-law is himself. The count is also married to his mum (he's a mormon or something, allowing multiple marriages). Thus his brother's father in law is himself. The count's mum is also married to his brother, thus the father-in-law's brother is himself. The count's sister is married to the count's son, thus the brother in law's father is himself.

O_o

• What a rude Count! – question_asker Mar 4 '16 at 14:00
• @question_asker Rude and lonely – manshu Mar 4 '16 at 14:01
• Not sure if I'm reading this wrong (it gets very confusing!) but being married to his brother's mother would only make him the brother's stepfather, not father-in-law. It does work if you say that his brother is married to their sister (spouse's [step]father). – feelinferrety Aug 7 '17 at 15:31

If we do not consider any incest or multiple marriages then answer is:

Three

Because his brother's father-in-law and his father-in-law's brother can be the same guy given that his brother marries a cousin of his wife.

Since text explanations can get really confusing really fast, I made a diagram to better visualize the relationships with the person(s) in question.

Key:

• Count = Red circle
• The father's brother-in-law = Green
• The brother's father-in-law = Pink
• The father-in-law's brother = Blue
• The brother-in-law's father = Orange