This is the last in a series of three exercices de style to show some interesting aspects of the game of hats: a puzzle which was initially proposed by Lionel Levine.
Here we look at case where each player has a tower of countably infinitely many hats on their head and try constructing efficient strategies from the results of the first exercice.
Guifred II comte de Cerdagne et de Confluent entreprit en 1001 de fonder l’abbaye Saint-Martin du Canigou. Sa pierre tumulaire en écriture onciale, perdue puis retrouvée dans le pavement de l’église de Casteil a été replacée dans son lieu d’origine en 2019 :
GUIFREDI COMITIS CINERES MONACHIQUE BEATI
ARTIFISQUE LOCI CONTINET ISTE LAPIS
FINE SUO IULIUS HUIC FINEM MILLE SUB ANNIS
BIS QUATER QUINIS CONTULIT ATQUE IX
La fonction factorielle est souvent définie comme le produit : $$n!=\prod_{k=1}^n k\text{,}$$ ou bien par récurrence : $$n!=n\cdot(n-1)!\text{,}$$ en prenant par convention : $0!=1$. Mais pourquoi cette convention ?
The Fifteen Puzzle consists of fifteen numbered square tiles in a 4×4 square grid, with one position empty or blank. Any tile horizontally or vertically adjacent to the blank can be moved into the blank position. The task is to rearrange the tiles from some random initial configuration into a desired goal configuration, ideally or optimally using the fewest moves possible.
Terschelling, The Netherlands, September 29 – October 1. Text of the paper available here.
A piece of retro-coding to which I contributed.
Back in 2004, VLC release 0.8 added cross-platform support for audio devices with PortAudio, and at last I was able to play quadraphonic streams1 on my hi-fi 😀
