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These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. In STM (slice turn metric), the minimal number of turns is unknown. There are many algorithms to solve scrambled Rubik's Cubes. An algorithm that solves a cube in the minimum number of moves is known as God's algorithm.
Solutions (not necessarily optimal) have been computed for every N ≤ 10,000. [2] Solutions up to N = 20 are shown below. [2] The obvious square packing is optimal for 1, 4, 9, 16, 25, and 36 circles (the six smallest square numbers), but ceases to be optimal for larger squares from 49 onwards.
Of these, solutions for n = 2, 3, 4, 7, 19, and 37 achieve a packing density greater than any smaller number > 1. (Higher density records all have rattles.) [ 10 ] See also
Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If a {\displaystyle a} is an integer , the answer is a 2 , {\displaystyle a^{2},} but the precise – or even asymptotic – amount of unfilled space for an arbitrary ...
The number of clusters chosen should therefore be 4. In cluster analysis, the elbow method is a heuristic used in determining the number of clusters in a data set. The method consists of plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to
Angel numbers are repeating number sequences, often used as guides for deeper spiritual exploration. Ranging from 000 to 999 , each sequence carries its own distinct meaning and energy.
And the numbers speak for themselves: Nvidia: if you invested $1,000 when we doubled down in 2009, you’d have $378,269 !* Apple: if you invested $1,000 when we doubled down in 2008, you’d have ...
For instance, let be a root of + + =, then the ring of integers of the field () is [], which means all + with and integers form the ring of integers. An example of a nonprincipal ideal in this ring is the set of all + where and are integers; the cube of this ideal is principal, and in fact the class group is cyclic of order three.