# Puzzle with twins

Dying someone appointed in the will the following: If his pregnant wife giving birth to a son , then she will inherit 1/3 of the estate and his son 2/3 . If giving birth to daughter , then she would inherit 2/3 of the property and the daughter 1/3 . The woman gave birth to twins after the death of her husband , a boy and a girl .How will be distributed the father's estate?

Any ideas or hints?

• I would simply say that the husband's will doesn't cover this situation, so there's no "correct" solution. – Jack M Nov 17 '15 at 19:09

The wording here is really bad and ambiguous, but the answer to this puzzle is that if

• the son inherits $4/7$ of the estate,
• the wife inherits $2/7$ of the estate, and
• the daughter inherits $1/7$ of the estate,

the proportions between wife-son ($1:2$) and wife-daughter ($2:1$) will still hold.

To find these values, translate the problem into equations: we want the wife to have two-thirds of what the wife and daughter share, and one-third of what the wife and son share. Also, the sum of their shares should obviously be $1$, i.e. everything. Altogether we have

$$\begin{cases}w = \frac 23 (w + d) \\ w = \frac 13 (w + s) \\ w+s+d = 1\end{cases} \iff \begin{cases}\frac 12 w = d \\ 2 w = s \\ w+s+d = 1\end{cases}$$

Plugging the 1st and 2nd equations into the third gives us $w + 2w + \frac 12 w = 1$, or $\frac 72 w = 1$, which means $w = \frac 27$. From there we can use the remaining equations to find $s$ and $d$.

• sorry for my bad english – Paris Lamp Nov 17 '15 at 15:46
• why son inherits $4/7$? – Paris Lamp Nov 17 '15 at 16:12
• Sorry, I added an explanation! Your English is fine -- it's just that the precise wording is tricky for this problem, as it only has a logical solution when you specify that it's about ratios between wife-son and wife-daughter, as opposed to parts of the whole estate. – Lynn Nov 17 '15 at 19:12

Isn't it much simpler to assign a value of 1 to the daughter, 2 to the wife and 4 to son? Adding those values totals to 7. The ratios are then easily derived by placing the assigned values over the total to yield:

1/7, 2/7 and 4/7