Tanya Khovanova

Never interviewed at Facebook but have been offered roles at similarly hard to get places. Though I am working at my own startup now, the absurdness of the interviewing process at majority of such places confounds me.

In short, I can't cope up with them well without going through quite a few glassdoor type questions of that respective company. And partially it is because most interviewers already have a set of solutions that they are looking for, and can't appreciate novel solutions and at times even better time/space complexity if they do not fit the standard mold. In my experience only some very hot startups had smart/ open enough interviewers to appreciate new solutions or see the relevance of new CS research results that may solve their question.

Before one starts attacking me on being a CS philistine, I want you to ponder on my background- current work involves designing & implementing pretty intricate & complex algorithms, and earlier research & publications in a range of ML related sub-fields, mainly NLP & recommender systems. I also read CS papers for pleasure, code in multiple languages and did reasonably well in programming competitions- no longer participate, latter is many years ago.

For a similar experience, though from a far more accomplished person, see Tanya Khovanova's blog post on hiring 'the smartest people in the world':
http://blog.tanyakhovanova.com/?p=402

Also, FYI I don't resent the system a lot. It is better than it being an old-boys-club; I just…

I loved the puzzle books, even though I wasn't very good at the puzzles. The titbit about his wife is this story (https://magazine.uchicago.edu/9506/June95BOBProfiles.html, NYT left out the actual puzzle)

> Smullyan admits the following puzzle might have come in handy had he designed it before meeting his wife.

> "I'll make a statement. If the statement is true, you give me your autograph. It doesn't have to be on a check, it can be on a blank piece of paper. If the statement is false, you don't give me your autograph," Smullyan sets up the puzzle. "Well, my statement is, `You will give me neither your autograph nor a kiss.'

And his puzzles always came with variations, like this (http://blog.tanyakhovanova.com/2010/05/raymond-smullyans-magic-trick/):

> Afterwards, Raymond Smullyan joined me in the elevator. “Do you want to see a magic trick?” he asked. “I bet I can kiss you without touching you.” I was caught off guard. At that moment I believed anything was possible. I agreed to the bet.

> He asked me to close my eyes, kissed me on the cheek and laughed, “I lost.”

And this bit from the preface to The Lady or the Tiger aptly summarizes most people's attitude towards maths:

> Before he called the boy to the phone, the
father said to me in soft conspiratorial tones: "He is reading
your book and loves it! But when you speak to him, don't let
him know that what he is doing is math, because he hates
math! If he had any idea that this is really math, he would
stop reading…

I suspect you've missed the point. When the answer is clearly 1/3 when the problem is this:

Take a room full of people. Ask them all to stand up.
Then:

Sit down if you don't have exactly two children.
Sit down if neither child is a boy.
What proportion of the remainder have two boys.

The problem is: what made the speaker say that in the first place? Under different assumptions you get different answers. This is akin to the problem:

Take a stick and break it at random into three pieces.
What is the probability the pieces can be used to make
a triangle?

Different people have different interpretations of what it means to say "at random."

Foshee's Tuesday-Boy question helps us see why this is an issue.

I have a child. One is a boy, born on a Tuesday.
What is the probability the other is also a boy?

Using the "obvious" reasoning the answer is 13/27.

I have a child. One is a boy, born on a Tuesday, plays the
piano, juggles, has red hair, and is left-handed. What is the
probability the other is also a boy?

Now the same reasoning as gave the answer 1/3 for the first version here gives the answer 1/2 - epsilon. To many this seems wrong, and highlights the importance of being explicit about the assumptions being made.

That's the point of the post, not the naive calculation.

See also Tanya Khovanova's post: http://blog.tanyakhovanova.com/?p=221

There's also a follow-up using Shannon entropy to…

AFTER EDIT: Thanks to all who have replied for the interesting comments. I discovered this link while digesting replies I received on three different email lists to a request to name experts on mathematically precocious young people. (That was for work.) Tanya Khovanova, the author of the blog post submitted here, was one name suggested to me as an expert on precocious mathematics learners. When I saw her personal website,

http://www.tanyakhovanova.com/

I remembered that I had seen her blog post "Should You Date a Mathematician?"

http://blog.tanyakhovanova.com/?p=319

posted to Hacker News (and other sites I read) before. I'll read more of her more purely mathematical blog posts over the next few days. I see one I can use right away in the local classes I teach to elementary-age learners.

On the substance of the post, I'm seeing several comments that equate "genius" to "person with a high IQ score." That was indeed the old-fashioned way that Lewis Terman (1877 to 1956) labeled a person with a high IQ score as he developed the Stanford-Binet IQ test. But as Terman gained more experience, especially with the subjects in his own longitudinal study of Americans identified in childhood by high IQ scores, he didn't equate high IQ to genius, and he became more aware of the shortcomings of IQ tests. Terman and his co-author Maude Merrill wrote in 1937,

"There are, however, certain characteristics of age scores with which the reader should be familiar. For one thing, it is…

Okay. To respond to both of you - I have put this in programming just to check, and I think you are taking a different inference from the question than I am.

Under your inference, the man wouldnt have mentioned anything unless he had at least one male child. (in which case you can say the GG scenario is gone, but GB BG and BB are equally probable)

Under my inference, the man just told me the sex of one child at random.... (in which case BB is twice as probable as GB or BG - where he could have equally said 'i have at least one girl')

That sound reasonable to you? I have it in ruby form if you are interested :)

The blogpost linked to by someone above (http://blog.tanyakhovanova.com/?p=221) uses this explanation, which is very different (to me) than the one in the main link, and I can see why this gets to 1/3:

"A father of two children is picked at random. If he has two daughters he is sent home and another one picked at random until a father is found who has at least one son."

The blog post[1] that the author based his short explanation on goes into this. Peter Winkler, a math professor at Dartmouth, is quoted in it[2]:

Suppose the puzzle is phrased this way: X says “I have two children and at least one is a boy.” What is the probability that the other is a boy?

Put this way, the puzzle is highly ambiguous. Computer scientists, cryptologists and others who must deal carefully with message-passing know that what counts is not what a person says (even if she is known never to lie) but under what circumstances would she have said it.

The way the puzzle is phrased, the only way to get 1/3 as an answer is to assume that parents with one girl will never say, "At least one of them is a girl."

1. http://scienceblogs.com/evolutionblog/2011/11/08/the-tuesday-birthday-problem/

2. http://blog.tanyakhovanova.com/?p=234