Today I have a logic puzzle based on the complex kinship rules found in Australian Aboriginal society. Aboriginal groups are divided into subgroups, called “skins.” Your skin is determined at birth, based on your parents’ skins, and it does not change in your lifetime. Your skin will determine certain social rules, such as who you marry.
The Warlpiri, who live northwest of Alice Springs, divide themselves into eight skins, according to the rules in the diagram below. Yes, it’s complicated! The skins are numbered 1 to 8. The horizontal rows indicate marriage correspondences, while the arrows point from mother to child. (All the marriages here are between men and women, and we can assume no divorces or half-siblings or step children.).
So, if your skin is 1, you must marry someone with a skin of 5, and vice versa, since both these skins are on the same horizontal line. If your skin is 2, you must marry a 6, and vice versa.
Similarly, if you are a female with skin 1, your children will be skin 4. If you are a female with skin 4, your children will be skin 2, and so on, following the arrows around.
For skin 1, males are Jakamarra, and females are Nakamarra. Likewise, the names of the other skins always begin with a J for men, and the J is replaced with an N for the women. (Except Jupurrula, which becomes Napurrula.) I’m not making any of this up, by the way.
Now imagine you go into a Warlpiri village and speak to six people about their family relations. Based on these responses, can you determine the female name for each of the skins?
“I am a Jangala. My daughter is Nampijinpa.” -
“I am a Nakamarra. My brother’s son is Jupurrula.”
“I am a Nampijinpa. My mother’s grandfathers were Jungarrayi and Jupurrula.”
“I am a Napangardi. My husband’s sister’s husband’s father’s father’s mother was Napurrula.”
“I am a Napanangka. Some of my good friends are Napaljarri and Nangala and Nungarrayi. Oh, you wanted me to talk about my family? Oops.”
“I am a Japanangka. My wife’s father’s mother’s brother’s wife’s father’s mother’s brother’s wife’s father’s mother’s brother’s wife’s father’s mother’s brother’s wife’s father’s mother’s brother’s wife’s father’s mother’s brother’s wife was Napurrula. I know my family tree very well.”
Even if you can’t do today’s puzzle – and it is quite tricky – at least you have learnt about Aboriginal kinship groups!
For mathematicians, extra points if you can tell me which dihedral group describes the relationship structure of the Warlpiri.
I’ll be back at 5pm UK with the answers.
Today’s puzzle was devised by Alan Chang, a maths PhD student at the University of Chicago, and appeared in the 2013 North American Computational Linguistics Olympiad. Alan got the idea when he did a class on Aboriginal languages while studying at the University of Melbourne.
PLEASE NO SPOILERS
(Hints are fine, as is a discussion of the ideas behind the puzzle and related issues, but please don’t write the answer.)
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
Christmas gift alert! In need of a present for a 7 to 13-year-old? May I suggest the Football School Box Set, containing Seasons 1-3 of my book series Football School that explains the world through the prism of football. The Premier League’s Head of Education said the series “will spark a love of learning in any child who reads it. It is intelligent, inspiring, funny, and deserves a large audience.” Peep peep!