Ham Mac Rom Oth Jul Lea 
A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice.
The nth centered hexagonal number is given by the formula
n
3
−
(
n
−
1
)
3
=
3
n
(
n
−
1
)
+
1.
{\displaystyle n^{3}-(n...
Python, 76 bytes
c=lambda n,k:k>1and'\n'.join(c(n-i,k-1)for i in range(n))or'987654321'[9-n:]
Caries out the procedure as described in the OP: joins the decreasing n results for k-1 on newlines with a base of the recursion of the 'n...1' string when k is 1 (k not greater than 1 since we are ...
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In the strategy game "Hexplode", players take turns placing tokens on a hexagonal board. Once the number of tokens equals the number of adjacent tiles, that tile hexplodes, and moves all of the tokes on it to the surrounding neighbors. You can play the game online here.
I like this game, but som...
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Output a sandpile
An abelian sandpile, for our purposes, is an infinite grid with integer coordinates, initially empty of sand. After each second, a grain of sand is placed at (0,0). Whenever a grid cell has 4 or more grains of sand, it spills one grain of sand to each of its four neighbors simu...
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry.
In mathematical contexts, duality has numerous meanings although it is "a very pervasive and important concept in (modern) mathematics...
