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## Double détente

C’est pas pire que si c’était moins bien.

Rien n’est plus difficile qu’expliquer une chose à une personne quand son salaire dépend de ce qu’elle ne la comprenne pas.1

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## Sudoku with red, yellow and blue

Each row and column must contain the digits 1-9. Digits may not repeat within the outlined regions. Digits may not repeat in cells of the same colour (except white). Digits outside the grid in red are colour sums. The value is the sum of all coloured cells (i.e. non-white) in that row / column. Digits outside the grid in black are sandwich clues. The value is the sum of all digits in that row / column between the 1 & 9.

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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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## Beautiful squares

Normal sudoku rules apply. Additionally, Kropki dots are placed in the grid. Kropki rules are applied only along the grey line (orthogonally or diagonally): adjacent cells containing digits whose difference is 1 are marked with a white circle; adjacent cells containing digits whose ratio is 2 are marked with Black circle; adjacent cells containing digits 1 and 2 may be marked with white or black circle. Adjacent cells with no marking must not contain digits whose difference is 1 or whose ratio is 2.

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## Christmas tree

Mark Goodliffe and Simon Anthony from cracking the cryptic are doing a fantastic job of making us discover the fascinating world of advanced sudoku.

Here is a treat for the season: normal sudoku rules apply, and identical digits cannot be a chess knight’s move apart. The grey square marks an even digit. Any two cages that share an edge and whose totals have a difference of 1 have a white dot between them, and any two cells that share an edge whose totals have a ratio of 2:1 have a black dot between them; there is a negative constraint so two cages touching each other without a dot do not have totals with a difference of 1 or a ratio of 2:1.

Please try the puzzle here.

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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.