Daphne is in a maze of tunnels shown below. She enters at A, and at each intersection, chooses a direction randomly (including possibly turning around). Once Daphne reaches an exit, she will not return into the tunnels. What is the probability that she will exit at A? The Idea At first, I will denote by […]

# Month: December 2020

## The Meaning Of It All

‘The Meaning Of It All’ is one of my favourite books written by the hero-physicist Richard P. Feynman. This book is a collection of three conferences Feynman held in 1963 at the University of Washington. He’s famous for the intellectual provocation he used to throw at the audience and for his clear way of speaking. […]

## Shortlist 2001/G1

Let be the center of the square inscribed in acute triangle ABC with two vertices of the square on side BC. Thus one of the two remaining vertices of the square is on side AB and the other is on side BC. Points and are defined similarly. Prove that lines and are concurrent. The Idea […]

## AI Artist

A nice programming challenge is writing a program that modifies an image to give using the style from another image, which in my case is Van Gogh’s Starry Night. Let’s take a look at the input image. A take of the houses of parliament at night. Now let’s see the output image after 7000 iterations. […]

## Guthrie Govan

One of my favourite guitarists is Guthrie Govan. He is a jazz fusion guitarist and his signature guitar is Charvel HSH FLAME MAPLE. His peculiarity is that is technique is so perfect he treats the guitar as part of his body: he is able to play with every technique. The very first Guthrie’s piece I […]

## The Solitude Of Prime Numbers

A very interesting Novel is ‘The Solitude Of Prime Numbers’, by Paolo Giordano. It talks about the story of Mattia and Alice, who both have some serious personal problems, and about how their relationship grows in time. I really appreciated how the author was able to continuatively switch points of view and put himself into […]

## Algebra At Christmas

Why not? I mean, it’s a nice inequality to try out. What if I asked you to find the maximum value of Well, time to apply the AM-GM inequality. First, let’s say that Notice that by the AM-GM inequality applied on the 4 positive real numbers Hence, we get that with equality when

## Tim Henson

Polyphia’s lead guitarist Tim Henson, is one of my favorite progressive metal guitarists. His signature guitar is Ibanez THBB10. He’s extremely creative and talent, and his peculiarity is that he can very easily create astounding riffs. For example check out this video. His signature technique is hybrid picking, and it’s thanks to him that I […]

## Blue Ocean Strategy

One of my favorite economy books so far is ‘Blue Ocean Strategy’, by W. Chan Kim and Renée Mauborgne. It is essentially a guidebook on how to create uncontested market space and make competition irrelevant. It is divided into 9 chapters, which explain the complete process of creating a start-up that is free from competition […]

## Shortlist 2006/A5

Let be the sides of a triangle. Prove that Always Try A Substitution We notice that the denominators are all positive, in fact by the triangular inequality. So let . Then . So we get applying in the last step. Similarly, we obtain Thus, now it is sufficient to prove that So let’s assume WLOG […]