Just for fun

I won a bronze medal in the XV Spanish Physics Olympiad held on March 19th-22th, 2004 in Vigo, Spain. Recently, I came across the exercises and I could not resist the temptation to solve it. It was funny to see exercises of such a level, including optics, quantum mechanics or heat transfer.

I won the silver medal in the local phase of the XXXIX Spanish Physics Olympiad held on 2003 in Seville.

The tower of Hanoi is a mathematical puzzle in which the goal is to move the entire column of disks from one tower to another under the restrictions that only one can be moved at the time and bigger disks cannot be on top of smaller ones. To solve it with two disks is trivial but... what about three? Just consider the set of the two smallest as a single disk. You got it? Let's go now for N disks!

This kind of algorithms are called recursive. Here you have a script, but try to solve it first on your own! If you want to play a bit in real time, visit this Geogebra applet. Enjoy!

Everybody knows what a Sudoku is, but sometimes one can struggle to solve it. There are several method but I explain here two of them. The first one is to fill a cell if only one number fulfils the restrictions and sweep among matrix once and again until it is solved. It may happen that despite the sudoku is solvable, the solution is not found because some guesses need to be done. Imagine starting with a blank sudoku. This algorithm will not even start. If the algorithm does not find it, it does not mean it has no solution. An alternative to this method consists of guessing between the possible values and continue sweeping. If one guess is proven invalid, it goes back and modify the guess. For this reason, the method is recursive. None of both method is exhaustive but the recursive one leads to a solution whenever it exists contrarily to the heuristic one.

You can download these algorithms here. If you want to know how recursive functions can help you solve nonlinear partial differential equations, visit our paper.