Last week, I finished plowing through Allen Downey's Think Stats. It took me about 5 days to work through it cover-to-cover. This book is great for those who need a crash course in using Python to do statistics. The conceit of the book is that it's a stats book for programmers. Hence, the statistics in it aren't past an upper-lever undergraduate level in difficulty. However, the programming required to work through the problems is at a higher level than I have seen in any other introductory stats book. I found it to be a great way to improve my Python programming. I worked through about 80% of the examples, skipping only those that were either trivial or did not seem relevant to my learning goals. For many of the examples, Downey provides .py files you can download from the book's website. I found that I usually took a different approach to solving problems than he did, but we most often agreed on the solutions. 

Anyway, the book is available as a free download and worth the time.

As I wrote a little while ago, I submitted a solution to IBM's Ponder this for February 2013. I was a bit of a pain in the butt since I first submitted an html file with no content. Oops. After sending the correct file, they reviewed it, and apparently my answer was suitable. You can see my name at the bottom of the webpage. Yay!

Tonight, I decided to work on this month's Ponder This problem. It reads as follows:

The brute-force solution to this problem is pretty straightforward. I used Mathematica, but any programming language will work. In this program below, I generate lists of x^2 and y^2 values. I then convert those numbers to strings, concatenate the strings, convert those strings back into a number and check if the square root (z) is an integer. The (x,y,z) values that meet this condition are stored in the checkres list. To check is z contains more than four 9's, I convert z back into a string and look for any substring within z that contains four of more 9's. The (x,y,z) values that fit this criteria are stored in the results list.

The major hurdle in this problem is figuring out where in x-y parameter space to search. For x<1,000 and y<1,000, the are no more than two consecutive 9's and computing time starts to become an issue in Mathematica. For 1,000<x<10,000 and 1,000<y<10,000, there are three z values with three consecutive 9's. For a language such as Python or C++, the computing time would be significantly faster. I chose Mathematica for the ease of moving between data types.

I have not had much luck reducing the parameter space for viable solutions. Below is the brute force Mathematica code to show solutions with two or more consecutive 9's. The x or y value is at least 5 digits. I found some reliable ways of general solutions with three consecutive 9's, but the four 9 solutions were elusive for longer than I care to admit. 

After looking at it for a while longer, I found that numbers of the form x=49999... and y=99999.... will produce an increaseing string of 9's in z when their squares are concatenated. Here are the solutions for four through eleven 9's. I'm sure there are solutions I am missing, but I believe this solves the problem as stated. 

Update: IBM has since posted an algebraic solution to this problem. They have not yet reviewed my solution since I accidentally sent them the wrong file at first.