Thursday, June 10, 2010

Mathematician in the Law School

Our most celebrated puzzle-solver, Kim the Ingenious, decided to attend a prestigious law school. With her sharp mind, clear logic and great persuasion abilities, she managed to convince the Law School administration to sign up for a deal. This deal would contractually oblige Kim to pay double the school fees, but only when she wins her first case. Until then, she would be required to pay nothing.
However, what Law School administration did not know was that Kim only ever intended to take on cases that she could not possibly win. As soon as she entered the Bar, she chose only those clients who have committed their crimes live on national TV and then sighed a confession in front of millions of people.

Unfortunately for Kim, the new dean of the Law School she attended, Prof Protagoras, was not prepared to tolerate her shenanigans any longer. The Professor came up with a plan every bit as devious as Kim's. He decided to sue Kim in court for the money she owes.

Professor does not expect the law school to win the case, but he believes that it will end up getting its money anyway. He reasons as follows: if Kim wins, then she will won her first case, which means she will be obliged to pay the amount she owes. If she doesn't win, then it means court has confirmed that she has to pay the money. Either way, Law School gets paid.

Needless to say, Kim does not see it quite like this. She believes that if she wins the case, it means the court has determined that she doesn't need to pay the money. If she loses, she has still not won her first case, which means that she is not obliged to pay. So, either way, the law school does not get paid.

Which of the two of them has got it right? And why?
This intriguing puzzle was adapted from a great book by J. Stangroom "Einstein's riddle."

Submit your answer on our Family Puzzle Marathon Be first to solve three puzzles and get a prize!


Katrina said...

I believe Kim did. If she is being sued and she is as smart and wily as protrayed, she would have another lawyer represent her during the court case. Therefore she would not get the credit for winning the case, her lawyer would receive it. After all a person who represents themselves has a fool for a client. And again, she still hasn't won a case so she shouldn't be required to repay the tuition yet.

Kim said...

Go me! Smart, wily, devious... I like Katrina's answer.

Maria said...

Wow, Katrina, what an interesting suggestion!
You go, girls! Katrina gets her well-deserved point and Kim keeps her tuition.

Tom said...

Tom appeals the decision! (Which was very cool.) Kim (and the Dean too) would have a lawyer if she's smart, and she is. Nonetheless Kim is the defendant in the lawsuit, and She will win or lose. That's ONE issue.

The other issue is, this is a court with a judge, and the Dean's suit is for money. It's a judge who will decide who is right (not logic alone), partly based on the contract, laws in her state, prior cases, and some common sense. And and in fact the judge will direct whether payment is to be made, and how much.

Anyway, what did Stangroom's book say, Maria?

Maria said...

It seems that Kim will be the winner anyway you look at it. Lawyers, beware of mathematicians! Strangroom's book says that this is a version of a dilemma known as the Paradox of the Court. However, the paradox is not completely hopeless.
A court should not find in favor of the Law School. Therefore, Kim wins or her lawyer wins a case for her. Depending how you would look at it, she may need to pay double her tuition. (Great thought, Tom!) However, the judge will likely award costs to Kim after her court victory. In that case the Law School would almost certainly owe Kim more than she owed it.

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