# Monthly Archives: May 2013

## Random matrices and pentagonal numbers

Here is a clever problem:

Let us fix $n$. Take at random, with uniform probability, a $n \times n$ binary matrix (call it $A$).
Let: $\gamma_n = P[\det_{Z_2}(A)=1]$.
(You can think of it as taking determinant of matrix normally and asking for a probability that it is odd number.)
Find the value of: $\gamma = \lim_{n\to\infty} \gamma_n$

(It’s not that gamma! Although, it is still related to Euler!)
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## About problem setting

I finally did it! In 2009-2010, I was helping the Codechef competitions to start.
I created more than 30 problems that were used across 12 different contests.
After, I got distracted (Master Thesis, PhD studies), and I stopped.
After those years, I finally took time to browse my local database of my problems and try and match them
with problems at Codechef. (I never uploaded them directly, it was always uploaded on spoj.pl, and then they were copied.) It was sometimes tricky, but I managed. I feel good about it, like when reconnecting after a long time with a friend. Here is the list of all of them.

What are my impressions about problem setting?
It is a perfect transition between participation in contests and work as a researcher. How so?
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