# 42 solved

Discussion in 'Physics & Math' started by Michael 345, Sep 9, 2019.

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3. ### Gawdzilla SamaValued Senior Member

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42 was the answer, not the problem.

5. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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Good point but not correct in terms of the article

Which was
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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?
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(-80538738812075974)3 + 804357581458175153 + 126021232973356313 = 42.
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My highlights pertinent parts

7. ### James RJust this guy, you know?Staff Member

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I haven't looked into this, but for me the interesting part would be the search algorithms that are used to narrow down the possible solutions. Obviously, this solution wasn't found merely by brute-force search.

The question that follows is then: is there a pattern here that we have some glimpse of, but not a complete solution for?

And the other, obvious question that I assume mathematicians would really like an answer to is:
Can every integer be expressed as the sum of three integer cubes?
Does this problem has a name? Is there a conjecture? How is progress going towards a proof, either way?

8. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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From what I understand they have solved 1 to 100 and now looking at numbers above 100.
Something about using private computers when not being used (like SETI)

9. ### Gawdzilla SamaValued Senior Member

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And we know which answer was most important, now don't we?

10. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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Yes

Nothing more important than Life, the Universe, and Everything

Gawdzilla Sama likes this.
11. ### TheFroggerValued Senior Member

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The solution should be simple using brute force computing:

(-10³<x<10³)+(-10³<y<10³)+(-10³<z<10³)

Of course you may have to extend the range of x,y and z, but I do not see why the solution involved such massive computer power.

12. ### James RJust this guy, you know?Staff Member

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According to what you have written here, that involves a brute-force check of 8 billion possibilities, and you're only checking numbers between -1000 and 1000 there.

Now, look at the actual answer for 42. One of the numbers there was 126021232973356313. That's $1.26\times 10^{17}$. To find that number by the same kind of brute-force search you suggest would require a check of $10^{36}$ possibilities, which is about 1 billion billion billion billion.

Are you still puzzled as to why massive computing power would be necessary? The actual problem is only about a billion billion billion times more complicated that you thought it was.

13. ### TheFroggerValued Senior Member

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Ahhh, okay JamesR. I see.