Tuesday, September 30, 2008

Putnam math competition

This is really cool. Tonight, I joined the kids here who will give this math test a shot in a few months. We had an overflow crowd at our first meeting.

The professor who's teaching us the ropes in weekly sessions is a great guy.

Here's one problem I did, from the promo poster:

Find the smallest natural number n which has the following properties:
(i) its decimal representation has a 6 as its last digit, and
(ii) if the last digit 6 is erased and placed in front of the remaining digits, the resulting number is four times as large as the original number n.

If n starts with 6, and n = 4k, then k must start with a 1. So:

n = 61 ..,

k = 1 ... 6

Now the cool part: some recursive long multiplication.

Multiplying 6*4 gives you 24, so 4 is the last digit of n. This means that 4 is also the second-to last digit of k. So 4*4 +2 = 18. 8 is the second-to-last digit of n, and third-to-last digit of k. We know that 1 is the second digit of n, so eventually, we have to get to a 1.

2
1....6
x4
61...4

1
1...46
x4
61..84

3
1..846
x4
61.384

25
153846
x4
615384


This is true. So I think that 153846 is the smallest n that ends in 6 where shifting the digits right gives you 4n.
I love this stuff.

My badass advisor

My academic advisor, I am glad to announce, is John C Bravman.

Not only is he my advisor, he is also the dean of my dorm complex, FroSoCo (”freshman sophomore college”, in true Stanford alphabet-soup style). Almost a decade ago, a prospective student wrote him a letter, asking him some questions about Stanford and addressing him as a “badass dean”. He later referenced this letter in a speech, and inadvertently gave himself a new title.

Today, Bravman is the Vice Provost of Undergraduate Education: the top-ranked suit in the undergraduate college. Whenever he walks out to address the student body in the Memorial Auditorium, my FroSoCo buddies and I chant “B-A-D… B-A-D… B-A-D…”, which stands for: “badass dean”. It has a nice ring to it, especially in the awesome acoustic environment of MemAud.

Mr. Bravman lives up to his badass name. He throws FroSoCo barbeques every Friday, hosts really interesting speakers at his house across the street on a roughly biweekly basis, and maintains a gigantic DVD collection that students can borrow from.

This is how I and four of my friends came to have Stanford’s one and only badass advisor. Once again, I can’t believe my luck.

Hello world

This is my first real blog. I started my freshman year at Stanford a week ago today, and it’s been fantastic. There are too many great things to do and not enough hours in a day to do them. So much is going on, in fact, that I think it’s high time for me to write a blog.

I’ll write about Stanford, about programming, about math, and about whatever looks fun or interesting to me.

Onwards…

 
Views