Business men, they drink my wine… A legal analysis of a joke from my grandmother

My grandmother sends me a great many e-mails.  It’s often quite useful as I can keep an eye on the sort of alt-right nonsense that somehow finds a home amongst our elderly.  I think of it as a window into the Grey Supremacist movement across the Anglosphere: insane conspiracy theories about how somebody, somewhere is getting money that should instead be going to retirees.

But she also sends me jokes and riddles.  Here’s one I received today:

A farmer died leaving his 17 horses to his three sons. When his sons opened up the Will it read:

My eldest son should get 1/2 (half) of total horses;
My middle son should be given 1/3rd (one-third) of the total horses;
My youngest son should be given 1/9th (one-ninth) of the total horses.

As it’s impossible to divide 17 into half or 17 by 3 or 17 by 9, the three sons started to fight with each other. So, they decided to go to a farmer friend who they considered quite smart, to see if he could work it out for them.

The farmer friend read the Will patiently, after giving due thought, he brought one of his own horses over and added it to the 17. That increased the  total to 18 horses.

Now, he divided the horses according to their fathers Will.

Half of 18 = 9. So he gave the eldest son 9 horses.
1/3rd of 18 = 6. So he gave the middle son 6 horses.
1/9th of 18 = 2. So he gave the youngest son 2 horses.

Now add up how many horses they have:
Eldest son  9
Middle son  6
Youngest son  2

TOTAL IS 17

Now this leaves one horse over, so the farmer friend takes his horse back to his farm.

Problem Solved!

That’s what I call scary Mathematics.

Problem, alas, is not solved.  But exploring why it isn’t solved allows me to talk about one of my favourite subject: self-help in law.

The mathematical trick is that 1/2 + 1/3 + 1/9 does not equal 1.  It equals a touch under 0.95.  We can be a bit more exact.  1/2 is equal to 9/18. 1/3 is equal to 6/18. And 1/9 is equal to 2/18.  Add up those fractions and you can see that the will accounts for 17/18ths of the horses.  1/18th of the horses has not been disposed under the will.

So what have the brothers done with the farmer’s help?  They’ve helped themselves to that additional 18th share of the horses that isn’t necessarily theirs.

First, we look to the will to see what is supposed to happen to ‘residue’: that property of the deceased that isn’t expressly directed to a beneficiary.  So the share in horses was to be distributed as above, but the residue might have gone to a charity, or another family member, or some other person.

But perhaps the above text is the entirity of the will. When a will is invalid or does not effectively dispose of all of the property, we talk about intestacy.  What’s a little bit scary is that each of the States and Territories of Australia have different rules about what is supposed to happen next.  This is quite terrifying: why is it that two families who are dealing with the complexities of intestacy in different areas of Australia have to navigate different legal frameworks?  Australia needs a single Administration and Probate Act to resolve these issues once and for all.

Imagine that the farmer died in the ACT.  We know from the pronoun that the farmer is male, and we assume that the three sons are alive.  What we don’t know is whether or not the farmer’s partner is still alive (or their gender). If they are still alive, we look to the Administration and Probate Act 1929 to see that we also need to know the status of their relationship.  And so and so forth.

We also need to know the value of the 1/18th share of the horses. We imagine that it is less than $200,000.  It could be that the partner was supposed to inherit the eighteenth share through the intestacy rules.

It’s true that, under the intestacy rules, the remaining eighteenth share might have been split evenly between the three brothers… but the farmer has caused a problem.

The farmer has added a horse to the property of the deceased.  He cannot simply remove the horse at the end of the process because the horse is no longer his.  Instead, that horse becomes part of the intestacy problem: you need to follow the rules to discover who is the new owner of the horse that was donated.

Imagine that the three brothers took equal share of the intestate estate (including the remaining eighteenth share).  The distribution would have been the simple division of 17 by their share, plus a third of the 18th share:

• Eldest: 8+ 1/2 horses, plus 17/(18×3) horses = 8 + 22/27 horses.  Note that this is still less than 9.
• Middle: 5+2/3 horses, plus 17/(18×3) horses = 5 + 53/54 horses. Note that this is still less than 6.
• Youngest: 1 + 8/9 horses, plus 17/(18×3) horses = 2 + 11/54 horses.  OH SHIT! THAT’S MORE THAN 2!

Old mate the farmer next door has shafted the youngest son his rightful 11/54th of a horse.  About 20% of a horse’s value.  The eldest and middle brother have both received more than they ought to have.

But things are worse now that the farmer has added in a new horse. Simple division of 18 by their share, plus a third of the 18th share:

• Eldest: 9 + 1/3 horses.
• Middle: 6 + 1/3 horses.
• Youngest 2 + 1/3 horses.

Basically, the youngest sues everybody and then everybody sues the intermeddling farmer.  The farmer never gets his horse back.

What’s more interesting about this story is that the brothers go to a friend rather than to a lawyer.  The Legal Australia-Wide Survey examines how people resolve their legal issues through quite an interesting research method.  What it found was that people have a lot of reasons not to go to a lawyer for help with their legal problems: perceptions of cost, time, and other difficulties means that people don’t get their legal needs met.  The three brothers are a good example of this: they needed legal advice but instead asked a savvy friend for their help instead.  The savvy friend made the problem several times worse, and shafted one of the brothers.  What started as a comparatively simple issue of law (but primary school level maths) ends up being extremely complicated law.