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Semi-log plot of solutions of + + = for integer , , and , and .Green bands denote values of proven not to have a solution.. In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum.
In January 1980 he improved his strategy to yield a maximum of 80 moves. Later that same year, he reduced the number to 63, and then again to 52. [ 11 ] By exhaustively searching the coset spaces it was later found that the worst possible number of moves for each stage was 7, 10, 13, and 15 giving a total of 45 moves at most. [ 16 ]
The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.
The Rubik's Cube world champion is 19 years old an can solve it in less than 6 seconds. While you won't get anywhere near his time without some years of practice, solving the cube is really not ...
However, draughts with only 5 × 10 20 positions [21] and even fewer, 3.9 × 10 13, in the database, [22] is a much easier problem to solve –of the same order as Rubik's cube. The magnitude of the set of positions of a puzzle does not entirely determine whether a God's algorithm is possible.
Subset sum problem, an algorithmic problem that can be used to find the shortest representation of a given number as a sum of powers; Pollock's conjectures; Sums of three cubes, discusses what numbers are the sum of three not necessarily positive cubes; Sums of four cubes problem, discusses whether every integer is the sum of four cubes of integers
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