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Nash equilibria in Ballmer's binary-search interview game
- moomin 2y agoOne day it is hoped that enough mathematicians will have worked on the problem to have finally, definitively answered Steve Ballmer’s interview question. The job will be shared between them.
- vlovich123 2y agoJust in time for the job to be replaced with AI.
- Onavo 2y agoWell, Terrence Tao is trying his very best to replace himself with an AI.
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- pfdietz 2y agoWhich, admittedly, seems like a much harder problem. A world in which AI churns out amazing proofs would be pretty radical though.
- Xcelerate 2y agoTerence is fascinating in how different his thinking is even from most other mathematicians.
- vlovich123 2y agoI think he’s trying to replace his grad students so that he can solve even more interesting problems.
- mekoka 2y agoThe real irony being that they show up to work just to discover that it was a software programming position.
- hehehheh 2y agoBut they can't quit once they taste that sweet total comp.
- drewcoo 2y agoThe "golden abacus" instead of "golden handcuffs?" Or as my undergrad mathematics advisor described friends who left academics for finance, "they spend their days clipping (stock) coupons instead of solving math problems - not as interesting but more interest."
- belter 2y agoRumor has it that Ballmer resigned after asking this question to a candidate named Aphyr...
- rileymat2 2y agoWith these types of trick questions, it is always interesting what is an acceptable trick and what is not. The question did not specify whole numbers as it does not specify a random selection, but one is in bounds and the other not.
- jhfdbkofdchk 2y agoI always felt that part of the interview process is the candidate asking clarifying questions as well as making and stating assumptions.
- mdswanson 2y agoIt is. Or at least it was for some of us. I didn't care if the candidate ever got the right answer. I cared about the thinking, the questions, the strategies, and the conversation.
- TZubiri 2y agoAnd if some interpretations lead to trivial solutions, but one leads to a complex problem, it's likely that their intention is the latter. A kind of tacit communication
- MarkusQ 2y agoActually, it may just as likely be that the interviewer is looking to see if you over complicate things. So _ask_.
- jnordwick 2y agoI hate that. It turns the problem into one of those lateral thinking puzzles we were told some basic information and then the answer winds up being something totally wildly different. It wasn't being very random in the end not being very productive
- kadoban 2y ago
- joshka 2y agoPrevious comments yonder: - https://news.ycombinator.com/item?id=41434637 https://news.ycombinator.com/item?id=41434637 - https://news.ycombinator.com/item?id=41463330 https://news.ycombinator.com/item?id=41463330
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- jnordwick 2y agoCan't this be solved to some sort of DP way of solving the sub problem? Do the payout between 0 and 1 as the percentage of the amount. With a range of 1 to 1 to pay off is obviously one With a range of 1 to 2 the payout is .5 At three values it becomes more interesting. There are two strategies for the candidate either a binary search for the endpoints. At four values you still have one level of binary search possible but after that it devolves down to the two value problem. At five values. If the interviewer thinks the candidate would choose binary search and it becomes too too value problems on each side after removing the middle element. There's definite problems with this but I wonder if he's already possible pay off matrix
- jonahx 2y agoIt's possible it could help but it wouldn't be lead to a typical clean DP problem, because you need the full mixed strategy vectors at each level. That requires N real numbers that sum to 1, for each player. Assuming you've found such a strategy for N, when you go to N+1 you still need to find the (N+1) element vector representing the probability that you select each number as your first guess, and you likewise need to know your opponent's probability vector for adversarially choosing a number. Once you guess at those vectors you can use your recursively built up DP sub-solutions to get the value of the game, but you are still stick with solving the optimization problem of finding those mixed strategy vectors for N+1, and will probably need something like CFRM or a similar technique to find them.