And its diagram is as follows:

6 × 3 = 18
Mother 1 → 3 shares
Grandfather 2 → 5 shares
Five brothers 3 → 10 shares (2 each)

Third case: the grandfather’s fixed one-sixth of the entire estate is more advantageous for him than either muqāsama or one-third of the remainder. An example is a husband, a mother, a grandfather, and two brothers—a situation in which the prescribed shares take up two-thirds of the estate, and the siblings exceed twice the grandfather in number by one, even if that extra heir were a sister.

Why the sixth is singled out here is that, after the husband’s half and the mother’s sixth have been assigned, two parts of the estate remain for the grandfather and the two brothers. A full sixth of the estate is undoubtedly larger than either a third of that remainder or a muqāsama share. One part, however, is still left over and cannot be divided between the two brothers. Therefore, the number of their heads (2) is multiplied by the original denominator of the estate (6), producing a new denominator of 12.

The resulting allocation is:
Husband: his original 3 parts become 6 shares out of 12.
Mother: her single part becomes 2 shares.
Grandfather: his single part likewise becomes 2 shares.
Brothers: their single part becomes 2 shares, so each brother receives 1 share.