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See https://www.sciencealert.com/the-sum-of-three-cubes-problem-has-been-solved-for-42?utm_source=ScienceAlert+-+Daily+Email+Updates&utm_campaign=eec218c916-MAILCHIMP_EMAIL_CAMPAIGN&utm_medium=email&utm_term=0_fe5632fb09-eec218c916-365669341
"Mathematicians have finally figured out the three cubed numbers that add up to 42. This has settled a problem that has been pondered for 65 years: namely, can each of the natural numbers below 100 be expressed as the sum of three cubes?

So the ultimate question must be: "If x3+y3+z3=k. K is each of the numbers from 1 to 100; what are x, y and z?

Douglas Adams must be smiling in heaven. For "those who came in late"as the used to say in Phantom comics: see
from the original TV series or from the not so good movie version:
 
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