"Announcing Pedant Tick and Duchess Pocket Posey of Canterlot!"
Princess Celestia was shaken out of her idle daydream by the Royal Guard's announcement. After the visit to Ponyville to oversee the School of Friendship (and pull a fast one on her former student - the prankster in her never really left her even in old age), she had returned to Canterlot to take care of all the scheduled Royal Visits. It seemed a slow day was in the cards.
Little did she realise that her foray in logic this morning was set to extend a little further.
The doors out of the throne room swung open, and in stepped a brown stallion with a black mane, dressed in a rather plain but still very formal-looking grey suit and tie, and his companion, a cream mare with a bright azure dress, entered the room.
"Duchess Posey," Princess Celestia acknowledged. "It's good to see you again. Are you and your new foal keeping well?"
"It's new foals, actually," Duchess Posey gave a small smile. "One filly and one colt each."
"Oh my, congratulations!" Princess Celestia gave her most adoring smile. "In that case, are THEY keeping well?"
"Healthy as you can imagine," Posey nodded. "But...it's also led to somewhat of a...complication, if you understand what I mean."
"Complication?"
The stallion who accompanied the Duchess, Pedant Tick stepped forward. "We seem to have reached an impasse regarding the late Duke Ring Rose's will, and we are unsure how to execute it."
"You see," sniffed Posey, wiping a tear from her eye, "as you know, my husband was terribly sick..."
"Ah yes, I do remember," Celestia lowered her head with a tinge of sadness. "It was his one regret, he said. Not being able to live to see himself become a father."
"Of course," Posey fetched a white handkerchief from the pockets of her dress, gave one sharp blow, before neatly folding it away. "Anyway, after he was gone, his will was read out. It said, and I quote, 'In the event that my wife bears a daughter, she is to inherit one third of my entire estate, while my wife is to inherit the remainder. In the event of my wife bearing a son, my wife will inherit one third of my entire estate instead, while my child inherits the remainder.'"
"Ah, I see," A look of understanding crossed Princess Celestia's face. "But you had both a son and a daughter, which complicates matters."
"It seems that he did not include a clause regarding the case of his wife giving birth to more than one foal," Pendant Tick said. "So as you can imagine, we are quite unsure as to what to make of it."
"Well, fear not," Celestia raised a hoof to her chin, deep in thought. "I believe I know of a way to divide the estate fairly while still keeping to the will's stipulations. What you need to do is..."
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Well you're on the right lines, non-action leading to new information on your part. I actually chose this one simply because other problems related to hats I internet-searched were one of like three variants, so I went with the LEAST popular iteration.
Off the top of my head.
Split the estate in half
Then follow the instructions of the will.
The first half is split so that the son gets 2/3 and the mother gets 1/3.
The second half is split so that the daughter gets 1/3 and the mother gets 2/3.
All together, the daughter gets 1/6, the son 1/3, and the mother 1/2.
Just as I was finishing that solution, another sprang up.
The son gets twice as much as the mother, and the mother gets twice as much as the daughter.
Daughter gets 1, mother gets 2, son gets 4.
1+2+4=7
Split the estate in 7.
Daughter gets 1/7.
Mother gets 2/7.
Son gets 4/7.
...Just split it into three evenly?
To quote the text:
A lawyer would surely notice the word "remainder". The daughter inherits 1/3 of the entire state, if born, and the mother inherits 1/3, if the son is born (which he is). So 1/3 to the mother, to the son and to the daughter.
Now to quote the author's note:
No remainder is mentioned, like, at all. So will it be giving the mother nothing or giving her everything?
This reminds me of a paradox, where one man asked an old lawyer to teach him the art of law. The lawyer agreed and asked in return: the apprentice were to be tested upon finishing the studying by trying to solve his first court litigation, and should he win the case, then the lawyer had taught him well and were expected to get paid for the teaching, and should the apprentice not, then he'd own the teacher nothing. The apprentice-to-be accepted the offer, and the teaching began.
As time passed, the apprentice had learnt everything a lawyer must know. He was to be put to the test, but he eluded his first trial. And seeing, that his apprentice seemed to be refusing to pay for the expectantly great teaching, the teacher initiated a litigation himself and blamed the apprentice of elusion from payment.
As the apprentice had appeared before the court, he defended himself: "If I lose this trial, pursuant to the deal I should not pay. Then again, if I do win, my teacher's argument will be invalid as per court decision. Therefore I should never pay".
The teacher, however, replied: "Quite on the contrary. Did we not agree? You would pay me, if you won the trial. If you lose this one, however, my argument will so be valid and you'll have to pay me anyway".
So who is right? As far, as I remember, the deal should not apply at all: who wants to win, will deduce his own victory. Therefore a more authoritative body shall decide, who's right.
So Celestia should nullify the will as not applying due to unclear inheritance conditions and divide the heritage however she deem fit.