Level two – part 2

Level 2(b): Two categories of heirs cannot share their portions of the estate AND there is no common divisor between the number of heads and the corresponding number of portions of BOTH categories i.e. they are parallel
Rule K: If the number of heads in both categories are the same, pick one and multiply it by the base number to get a new base number

Example 20

Heirs 2 Wives 2 Full sisters 2 Consanguine brothers
Shares ¼ 2/3 Residue
Base number 12
Portions 3 8 1
Number of heads 2 2 2
New base number 24
New portions Each = 3 Each = 8 Each = 1

The two full sisters can share the 8 portions allotted to them such that each gets 4 portions. But 2 wives cannot share 3 portions of the estate. Likewise, 2 consanguine brothers cannot share 1 portion. Meaning that, we have 2 categories of heirs that cannot share their portions. That is the first criteria of applying the rules of Level 2(b). The second is that the number of heads and the corresponding number of portions of BOTH categories MUST be parallel.

The example above also fulfils the second criteria in that the category “wives” has 2 heads and 3 portions. 2 and 3 are parallel since they have no common divisor. Similarly, 2 and 1, the number of heads and number of portions of category “consanguine brothers” respectively are parallel! But WHY is the number of heads of consanguine brothers said to be 2? If every male has “2 heads,” then the total number of heads of 2 consanguine brothers should be 4! Yes, very true. But recall the point noted in Example 2; that if all heirs are male, each should be considered as having “1 head” so as to reduce the base number. The principle also applies when ALL heirs in a category are male. Thus, the number of heads of 2 consanguine brothers HERE is 2 since only the two of them make a category. There is no female among them.

Now, applying Rule K, the number of heads of both categories that cannot share their portions are the same. So,
New base number = 2 × 12 = 24
New portion of wives: 24 × ¼ = 6
New portion of 2 full sisters: 24 × 2/3 = 16
New portion of 2 consanguine brothers: 24 – (6 + 16) = 2
Each wife, full sister and consanguine brother inherits 3, 8 and 1 portions respectively.

Rule L: If the number of heads in one category is a multiple of the number of heads in the other category, use the higher number to multiply the base number so as to generate a new base number

Example 21

Heirs 2 Wives Daughter 4 Half uncles
Shares 1/8 ½ Residue
Base number 8
Portions 1 4 3
Number of heads 2 1 4
New base number 32
New portions Each wife = 2 16 Each uncle = 3

The categories that cannot share their portions are “wives” and “half uncles” because in the former, 2 wives cannot share 1 portion, while in the latter, 4 half uncles cannot share 3 portions. Also, 2 and 1 are parallel, just as 4 and 3 are parallel. Now, looking at the number of heads in both categories, 4 is a multiple of 2, so we pick the higher one, 4. Therefore,

New base number = 4 × 8 = 32
New portion of 2 wives: 32 × 1/8 = 4
New portion of daughter: 32 × ½ = 16
New portion of 4 half uncles: 32 – (4 + 16) = 12

Note that the number of heads of 4 half uncles suppose to be 8, but given that there is no female among them, each one is considered as having “1 head.” Assuming 8 was used instead of 4; the problem should have been solved like this.

Heirs 2 Wives Daughter 4 half uncles
Shares 1/8 ½ Residue
Base number 8
Portions 1 4 3
Number of heads 2 1 8
New base number 64
New portions Each wife = 4 32 Each uncle = 6

Number of heads of “half uncles” category, 8, is a multiple of 2, the number of heads of “wives” category. As a result, 8 is chosen. Thus,

New base number = 8 × 8 = 64; which is more than the 32 earlier gotten.
In line with this, let’s revisit Example 20 and use 4 as the number of heads of the 2 consanguine brothers instead of 2. By doing that, Rule L will be applied rather than Rule K. So,

Heirs 2 Wives 2 Full sisters 2 Consanguine brothers
Shares ¼ 2/3 Residue
Base number 12
Portions 3 8 1
Number of heads 2 2 4
New base number 48
New portions Each = 6 Each = 16 Each = 2

As in Example 21, the number of heads of “consanguine brothers” category, 4, is a multiple of 2, the number of heads of “wives” category, hence 4 is picked, being the higher number.

New base number = 4 × 12 = 48; which is also more than the 24 earlier gotten.

Therefore, it is evident that in both cases, the new base number is doubled when each male in an exclusive male category is considered to have “2 heads.” And as the principle of base number is that the MINIMUM is always chosen, the previous solutions are hereby retained. This further buttresses the fact that males are believed to have “1 head” when they are the only heirs OR when they are the only ones in a category!

Rule M: When the number of heads in both categories is parallel, multiply them; then multiply the answer by the base number. The result obtained is the new base number

Example 22

Heirs 2 Wives 3 Uterine sisters Full brother’s son
Shares ¼ 1/3 Residue
Base number 12
Portions 3 4 5
New base number 72
New portions Each = 9 Each = 8 30

2 wives cannot share 3 portions and 3 uterine sisters cannot share 4 portions of the estate. In both categories, number of heads and number of portions are parallel. That is, 2 and 3 for wives and 3 and 4 for uterine sisters respectively. Also, the number of heads in both categories, 2 (wives) and 3 (uterine sisters) are equally parallel. Hence,

New base number = 2 × 3 = 6 × 12 = 72
New portion of 2 Wives: 72 × ¼ = 18
New portion of 3 uterine sisters: 72 × 1/3 = 24
New portion of Full brother’s son: 72 – (18 + 24) = 30

Each wife and uterine sister is given 9 and 8 portions respectively, while full brother’s son receives 30 portions.

Rule N: If the numbers of heads of the two categories that cannot share their portions have a common divisor, divide ANY of them by the common divisor, then multiply the result by the OTHER. Finally, multiply the solution obtained by the base number. The end result gives the new base number

Example 23

Heirs 9 Daughters 6 Uterine brothers
Shares 2/3 1/3
Base number 3
Portions 2 1
New base number 54
New portions 4 apiece 3 apiece

Both categories cannot share their portions. In addition, the number of heads and number of portions for both categories (i.e. 9 and 2; 6 and 1) are parallel. But considering the number of heads 9 and 6, they have a common divisor, 3. Consequently,

New base number = 9 ÷ 3 = 3 × 6 = 18 × 3 = 54; alternatively,
New base number = 6 ÷ 3 = 2 × 9 = 18 × 3 = 54
New portion of 9 daughters: 54 × 2/3 = 36
New portion of 6 uterine brothers: 54 – 36 = 18
Each daughter and uterine brother gets 4 and 3 portions respectively.

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