From the original base the mother’s single share is multiplied by six, becoming six, and the remaining five shares are likewise multiplied by six, becoming thirty. Of these thirty the grandfather, by co-division, takes ten, leaving twenty. The full sister then receives one-half of the estate, that is, eighteen, so two shares remain for the paternal brother and paternal sister. Their heads are three, which neither divide evenly nor correspond with what is left, so we multiply the three heads by the thirty-six, yielding a new base of one hundred and eight.
Thus:
– The mother’s six shares × 3 = 18.
– The grandfather’s ten shares × 3 = 30.
– The full sister’s eighteen shares × 3 = 54.
– The paternal brother and sister’s two shares × 3 = 6, divided as four to the brother and two to the sister.
Next we notice that every portion and the corrected base share the common factor of one-half; accordingly the problem is reduced to its half, fifty-four. The full sister’s portion therefore falls to twenty-seven, the grandfather’s to fifteen, the paternal brother’s to two, and the paternal sister’s to one.
Schematic layout:
6/6 26/3 108 54
Mother 1 6 18 9
Grandfather 10 30 15
Full sister 5 18 54 27
Paternal brother 4 2 3
Paternal sister 2 1
- Zayd’s “Ninety Case.” Its heirs are a mother, a grandfather, a full sister, two paternal brothers, and a paternal sister. It is so called because the case is correctly resolved on a base of ninety. The reason it balances on ninety is that the grandfather’s most advantageous share here is one-third of what remains after the mother’s one-sixth; accordingly, the root of the problem would be eighteen if that third of the residue were taken along