# Did you solve it? An Aboriginal family puzzle

Earlier today I set a following puzzle: Aboriginal groups are split into subgroups, called “skins.” Your skin is decided at birth, determined by your parents’ skins, but it won’t difference in all of your life. Your skin determines certain social rules, including what you do allowed to marry.

The Warlpiri, who live northwest of Alice Springs, divide themselves into eight skins, as per the rules in the diagram below. Yes, it’s complicated! The skins are numbered 1 to 8. The horizontal rows indicate marriage correspondences, as you move the arrows point from mother to child. (The many marriages here i will discuss between men and women, and now we can assume no divorces or half-siblings or step children.).

So, if your skin is 1, you need to marry someone by using a skin of 5, and or viceversa, since both of these skins have a similar horizontal line. But if your skin is 2, you have to marry a 6, and the other way around.

Similarly, an advanced female with skin 1, your sons or daughters will probably be skin 4. If you’re an female with skin 4, children is going to be skin 2, and many others, adopting the arrows around.

For skin 1, the male is Jakamarra, and females are Nakamarra. Likewise, what they are from the other skins always get started with a J males, and the J is substituted with an N for your women. (Except Jupurrula, which becomes Napurrula.) I’m not really earning any for this up, mind you.

Now imagine you’re going towards a Warlpiri village and talk to six people regarding their family relations. Dependant on these responses, could you determine the woman track record every one 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. A handful of my best friends are Napaljarri and Nangala and Nungarrayi. Oh, you wished me to speak 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 understand our family tree perfectly.”

Solution:

The female names for that skins are: 1. Nakamarra, 2. Nampijinpa, 3. Napanangka, 4. Nungarrayi, 5. Napaljarri, 6. Napangardi, 7. Napurrula, 8. Nangala.

Explanation:

Let’s first master how to use the diagram.

• To receive husband to wife (H2W), or or vice versa (W2H), move across to another side on the row.

• To receive mother to child, move on the arrow. (M2C)

• To get from child to mother, move down the arrow backwards. (C2M)

• To receive father to child, move across to another side from the row, after which it over the arrow. (F2C = H2W and M2C)

• To receive from child to father, move along the arrow backwards and after that over the row. (C2F = C2M and W2H)

• All siblings have the identical skin, merely because share the same mother. (SIB)

STEP 1. Could Nakamarra is 1 ,review start with sentence (ii). And let’s break it down. It’s saying: If I am 1, then in case you apply the rule for brother, then this rule for father to child, you will enjoy Jupurulla.

1 > SIB > F2C = Jupurulla

[The ‘>’ sign shows the direction in our deduction]

1 > 1 > 7 = Jupurulla. Skin 7 is Jupurulla for males, and thus Napurrula women.

STEP 2. With knowledge that Napurrula is 7, let’s pay a visit to (iv). It truly is saying:

Napangardi > W2H >SIB > W2H > C2F > C2F > C2M = 7

But we could go the other excessively:

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 glance at the daunting statement (vi). If you look closely it really is repeating the idea ‘wife’s father’s mother’s brother’ several times. This can be a relation:

H2W > C2F > C2M > SIB, which simplifies as

H2W > C2M > W2H > C2M, you may possibly notice always goes time for the places you started! (A result of the symmetries with the arrows). So that we can ignore all appearances of “wife’s father’s mother’s brother” and therefore are left with

Japanangka > H2W > 7. So Japanangka is 3 (male), therefore the 3 (female) is Napanangka.

STEP 4 Now to statement (iii). The problem suggestions we have 2 types of grandfather (maternal and paternal) and that we have no idea what design is Jungarrayi and what kind is Jupurrula (7).

(iii) says:

• Nampijinpa > C2M >C2M > C2F = 7 or Jungarrayi. (maternal)

• Nampijinpa > C2M > C2F > C2F = 7 or Jungarrayi. (paternal)

By performing exercises the number of choices we see whenever 7 could be the (mother’s) paternal grandfather, then Nampijinpa is a 6, and that is already taken. So 7 has to be the (mother’s) maternal grandfather, therefore Nampijinpa is 2 and Nungarrayi is a 4.

STEP 5. It is all joining together. From (i) Jangala has to be male skin 8, so Nangala is female skin 8. Leaving Napaljarri for the reason that 5.

OOF!

Extra points if you spotted which the kinship system is D4, the dihedral group of order 8, the particular gang of symmetries of the square. (Going from husband to wife or or vice versa is similar to flipping the square over, all night in the four skins 1-4-2-3-1, or 5-7-6-9-5 is similar to rotating the square 90 degrees each and every time.)

I we imagine you enjoyed the puzzle. I shall be instruction online fourteen days.

I set a puzzle here every 14 days over a Monday. I’m always within the look-out for great puzzles. If you wish to point out one, email me.

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