Yeah, I found the site when I was looking for material to study for the Putnam. It is a great site for learning about advanced math topics and even finding more challenging pre-college math material, by the way.
> Of course, you can't offer the guy infinity dollars. So the interviewee is forced to either settle on a real world number—as much as the player can afford—or delve into marginal utility theory
I don't think that as much as the player can afford is a real world answer, unless it means as much as the player can afford to lose. There is a 50% chance he'll walk away with $1. As Wall Street have proven, it's not about maximizing expected returns, it's about optimizing returns within bounds of acceptable risk.
But you're playing the house to his Martingale bet, right? If the game was repeated, you should be willing to bet all your money on it, since the odds are in your favor.
I think the question checks your ability to understand the mathematical potential payoff, but also to weigh that against the real-world consideration of risk.
I suppose. But there's a difference between "mathematical potential payoff" and how much I will risk on the flip of a coin. And as far as I can tell, the amount I pay has no effect on the odds or rules. So, three bucks.
Oh, absolutely, and that's the point of the question. My guess is that the answer "three bucks" and the answer "Well, the expected payoff is infinite, but ... three bucks" is the difference between the door and an offer.
I agree with you. Unless I misunderstood the question; the theoretical "right" answer is just wrong.
Let's make it more practical.
There is 100k in the table. A guy tells you, head you double the money, tail, you stop, and get what is there, but you have to pay a fee.
Obviously, up to 100k for the fee, it is no brainer, head you end up with at least 200k, tail, you go home with 100k, same as the fee you paid.
BUT: are you willing to pay 120k? 150k? Mathematically, you should, as the probablity of winning is a lot larger, but realistically you have 50% chance that you might loose 50k right away.
Assuming that all your savings are 100k, would you have the stomach to a accept this risk?
Most normal people, probably not. But according to this lawfirm, you should. Maybe this thinking got us in trouble in the first place.
"Last night I sat behind two wizards on a bus, and overheard the following:
A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.
B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?
A: No.
B: Aha! AT LAST I know how old you are!
I don't think you understand the problem. Even if you manage to find 4, 4, 3, 1 and 6, 2, 2, 2, you still have to verify that if the sum is 12, then there is only 1 possible product. You'll note that nobody in the linked thread succeeds at this (one guy proves that 12 works by exhaustive search, not really a possibility in an interview...)
Well, I saw it before, and it took a several minutes then, maybe 5 or 15, I don't really remember. Then you have to consider that companies like D.E. Shaw end up hiring people who would end up giggling at how long somebody slow like me would take to solve the problem.
it's also a Slate article vs. HN. i'd expect them to post questions that dazzle the least common denominator, while still allowing them to understand what's going on after a brief explanation. i'd be worried if HN _couldn't_ solve problems understandable by Slate's target audience.
Um, can someone explain the answer to the first question? Why wouldn't it go lower than the low eighties? Or higher, for that matter? How would the price change if there were 1000 sellers?
Basically the sellers end up bidding for the opportunity to sell. So basically some sellers won't be willing to sell below 89, more won't be willing to sell below 88, and even more won't be willing to sell be 87. And it works the other way too, so the lower the price gets, the more people are willing to buy. So theoretically, when the number of buyers equals the number of sellers, transactions end up occurring. This is assuming that the market is efficient, which isn't always the case.
If there were 1000 sellers, the price would drop even lower, because there is more competition among the sellers.
The point of the question is that there is no mathematically "right" answer. The interviewer knows the answer from experience, and (s)he's testing two things: whether the interviewee's intuition on the market is right, and, if not, how well the interviewee takes to being corrected.
Your answers are "right", in that they are possible, but they are not the numbers the interview wants to hear.
That makes more sense. I thought there was some obvious game theory principle I was missing, since somebody commented that they could answer the question without knowing anything about trading.
http://www.artofproblemsolving.com/Forum/index.php
Rusczyk always has something interesting to say.