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Recently on LinkedIn, someone posted the following brain teaser:

What's the remainder when 100100 is divided by 11?

I thought of the answer, but couldn't figure out why it was true, which stressed me out some (thinking that something like this might come up at an interview, and wanting to be able to look good on such a question). After some anxious moments, I finally came up with a method of solving the problem that validated my answer in a more general way. (It involves rewriting the expression as (99 + 1)100, doing a binomial expansion, and noting which terms vanish in the expansion.)

I was pleased with the solution, because it involved two important problem-solving techniques: Polya's solving a simpler problem (in this case, working with 99 which is divisible by 11), and Zeitz' "restating" the problem (expressing 100 as 99 + 1). (If you recall, Zeitz is the Stuy grad who authored the problem solving book I wrote about some time ago.) And it's something I can use to solve many other similar types of problems.

So, it's happening (finally!!). I'm getting better at problem solving; back to my old self, sort of. There's still a ways to go, but I can see the work of the past few years starting to pay off some. Hopefully I won't get completely stuck on these types of interview questions.

Speaking of which, two Google recruiters have contacted me in the past two weeks. Based on some things I've read, this is becoming a fairly common occurrence. There are hordes of contract/freelance recruiters combing all the social networking sites, tech user groups, etc., looking for candidates. (So why are so few people being hired, and Google is claiming they can't find qualified people? A subject for a future post.) But if Google (or someone else) did make me an offer in the next few weeks, that would create a huge dilemma. My trip to France is less than five weeks away ...



( 4 comments — Leave a comment )
Jun. 10th, 2007 01:47 am (UTC)
Did you ever meet Paul Zeitz? He was the captain of the math team in the year our tenures overlapped ('74-'75). I learned quite a bit from him.

Good luck getting a nice offer! I'm sure most employers would be fine with your taking your already planned vacation.
Jun. 10th, 2007 02:21 am (UTC)
I never met Paul Zeitz.

Re: taking vacation, we'll have to see, I guess. I probably won't be the only candidate for any job I get in the immediate future, and it's highly likely that the other candidates will want very badly to work at some Silicon Valley company. (Especially if they're here on visas.) So I have to at least anticipate the possibility that a company would want me to start right away with no vacation.
Jun. 11th, 2007 04:26 am (UTC)
is it 1? 100 = 1 (mod 11), so 100^100 = 1^100 (mod 11) = 1 (mod 11).
Jun. 11th, 2007 05:45 am (UTC)
Yes. That's the first thing I thought of, but got anxious trying to figure out why it was true. There are a lot of algebraic identities that are similar, but because I haven't done any algebra since 1990, I get them confused. Fortunately, I was able to figure out another way to solve the problem. I feel more at ease when I have multiple ways of figuring things out, like a quarterback who has options to throw to one of several receivers, hand off to a back, or run.

The modular arithmetic Wikipedia page is helpful in this regard.

Getting stuck on something like this on an interview makes me look like I don't know what I'm talking about, or that I'm trying to puff up my résumé.
( 4 comments — Leave a comment )