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## La pensée en mouvement

Les Mathématiques et la pensée en mouvement : une belle conférence d’Alain Connes.

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## Robust super-resolution depth imaging

Robust super-resolution depth imaging via a multi-feature fusion deep network — arxiv.org/abs/2011.11444.

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## Many lifes

Conway’s Game of Life, emulated in Conway’s Game of Life. The Life pattern is the OTCA Metapixel. The life simulator used is Golly.

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## Infinitely Many Hats (3/3)

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.

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## 0! = 1

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 ?

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## Classic 15 Puzzle

15-puzzle by Mark Rohlich

## Genesis

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.

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## Towers of hats (1/3) A towering pillar of hats (number $4$)

This is the first 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, and arose from his work with Tobias Friedrich on

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## Schizo: a different sudoku solving technique

Over the years, several tips and techniques have been developed to help solve sudoku puzzles with logic rather than brute force. To name a few, sudoku9x9 mentions (among others) hidden single, naked single, x-wing.

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## IMO 2019 Problem 1

An exercice with MathJax

Problem 1: Let $\mathbb{Z}$ be the set of integers. Determine all functions $f : \mathbb{Z} \rightarrow \mathbb{Z}$ such that

\begin{equation}
\forall (a, b) \in \mathbb{Z} \times \mathbb{Z}, \quad f(2a) + 2 f(b) = f(f(a + b))
\label{eq1}
\end{equation}

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