Earlier today I set you the following puzzle: 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 are allowed to 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) “I am a Jangala. My daughter is Nampijinpa.” –
(ii) “I am a Nakamarra. My brother’s son is Jupurrula.”
(iii) “I am a Nampijinpa. My mother’s grandfathers were Jungarrayi and Jupurrula.”
(iv) “I am a Napangardi. My husband’s sister’s husband’s father’s father’s mother was Napurrula.”
(v) “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.”
(vi) “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.”
The female names for the skins are: 1. Nakamarra, 2. Nampijinpa, 3. Napanangka, 4. Nungarrayi, 5. Napaljarri, 6. Napangardi, 7. Napurrula, 8. Nangala.
Let’s first get the hang of how to use the diagram.
To get from husband to wife (H2W), or vice versa (W2H), move across to the other side of the row.
To get from mother to child, move along the arrow. (M2C)
To get from child to mother, move along the arrow backwards. (C2M)
To get from father to child, move across to the other side of the row, and then along the arrow. (F2C = H2W and M2C)
To get from child to father, move along the arrow backwards and then across the row. (C2F = C2M and W2H)
All siblings have the same skin, since they have the same mother. (SIB)
STEP 1. We know Nakamarra is 1 ,so let’s start with sentence (ii). And let’s break it down. It is saying: If I am 1, then if you apply the rule for brother, then the rule for father to child, you get Jupurulla.
1 > SIB > F2C = Jupurulla
[The ‘>’ sign shows the direction of our deduction]
1 > 1 > 7 = Jupurulla. Skin 7 is Jupurulla for men, and thus Napurrula for women.
STEP 2. With knowledge that Napurrula is 7, let’s go to (iv). It is saying:
Napangardi > W2H >SIB > W2H > C2F > C2F > C2M = 7
But we can go the other way too:
7 > M2C > F2C > F2C >H2W > SIB > H2W = Napangardi
7 > 6 > 3 > 6 > 2 > 2 > 6 = Napangardi. So Napangardi is Skin 6.
STEP 3 Let’s now look at the daunting statement (vi). If you look closely it is repeating the phrase ‘wife’s father’s mother’s brother’ several times. This is the relation:
H2W > C2F > C2M > SIB, which simplifies as
H2W > C2M > W2H > C2M, which you may notice always takes you back to where you started! (Due to the symmetries of the arrows). So we can ignore all appearances of “wife’s father’s mother’s brother” and are left with
Japanangka > H2W > 7. So Japanangka is 3 (male), so the 3 (female) is Napanangka.
STEP 4 Now to statement (iii). The issue here is that we have two types of grandfather (maternal and paternal) and we dont know which one is Jungarrayi and which one is Jupurrula (7).
By working out the possibilities we see that if 7 is the (mother’s) paternal grandfather, then Nampijinpa is a 6, which is already taken. So 7 must be the (mother’s) maternal grandfather, and thus Nampijinpa is 2 and Nungarrayi is a 4.
STEP 5. It’s all coming together. From (i) Jangala must be male skin 8, so Nangala is female skin 8. Leaving Napaljarri as the 5.
Extra points if you spotted that the kinship system is D4, the dihedral group of order 8, which is the group of symmetries of a square. (Going from husband to wife or vice versa is like flipping the square over, and going through the four skins 1-4-2-3-1, or 5-7-6-9-5 is like rotating the square 90 degrees each time.)
I hope you enjoyed the puzzle I’ll be back in two weeks.
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.