MHB Is the Sum of Three Cubes Solved for the Number 33 by a Planetary Supercomputer?

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The sum of three cubes problem for the number 33 has been solved using advanced computational methods, specifically by a planetary supercomputer. This breakthrough adds to the recent resolution of the same problem for the number 42, which is famously associated with the meaning of life in popular culture. The findings highlight the capabilities of modern computational power in tackling complex mathematical challenges. The solutions for both numbers demonstrate significant progress in number theory and computational mathematics. This development continues to spark interest in the mathematical community regarding the properties of cube sums.
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Additionally, the number 42 was solved just a little bit later.
It's already mentioned in the article you refer to as an Editor's Note.

So a planetary supercomputer solved the problem of the number 42, finally giving meaning to Life, the Universe, and Everything.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

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