# 42 is the sum of three cubes

Originally published at: https://boingboing.net/2019/09/06/42-is-the-sum-of-three-cubes.html

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This is wonderful news.

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Got a friend who turns 42 next week. Will send him that. Also, something to disinfect his phone with.

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Now that this calculation is complete, does it mark the end of Life, the Universe and all the rest?

Thanks for the fish

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1x1x1 = 1 (first cube);
1x1x1 = 1 (second cube);
1x1x1 = 1 (third cube).
The sum of the three cubes is THREE.

In what number system does the sum of these three cubes fall within 3 units of the number 9?

3 is within 3 of a multiple of 9, specifically 9 times 0.

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Alright we fer-filled our planet life purpose. Time to die and give the Mice there planet back.

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“Every cube of a whole number is within one of a multiple of nine, which means that a sum of three cubes must be within three of a multiple of nine.”

Hate to argue semantics, but what is math if not expressions, syntax --semantics?

For the sum of three cubes to fall WITHIN three units of any “multiple of 9” …(let’s use zero, as you suggested) … then 0 must be <3

3 is not < 3
and 3 is therefore NOT “within three of a multiple of nine.”

using the mathematical definition of within, 0 & 3 are both within the set of 0-3

``````0    1    2    3
|----|----|----|
``````

(the length of one space is the distance of a whole integer, hence 0 and 3 are exactly 3 whole integers apart, which is why 0+3 = 3, it’s also what the number 3 means, any number is itself from 0 by definition of being a number so it’s not a very informative distinction.)

all numbers are 1 (whole integers) apart, not 0.¯9 apart

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Nothing like math articles to bring out the pedants. 0.999…=1, btw. Just saying.

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Ah. The answer to life, the universe and everything.

Bother bother bother…

Having 42 as the last number with an unknown solution for a numbers less than 100 was a good story, 33 having recently been solved as the second last. I enjoyed digging out the papers on this one to understand the problem; classic number theory stuff. I was very unsatisfied with the proofs that a solution is known not to exist for all whole numbers that leave behind a remainder of 4 or 5 when divided by 9.

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But there’s clearly five of them.

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I see Zappa back there also.

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41 is the sum of five dudes…

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dont panic. im sure other earths will continue the work after ours is reset, and or paved over

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42 is the number of angels that can dance on the head of a pin, a type of Christian “argument” that shows the absurdity of such a notion.

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It’s unnatural, sez I.

Electric cars, human-monkey hybrids, and now this… what was wrong with numbers being the sum of two addends the way our lord and savior intended? 1+1=2, 2+2=4… those are good, wholesome sums. Three terms? That’s just perverted is what it is.

Damn boffins, always asking if they can, never asking if they should.

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Warning: the provably smallest solution uses 80-digit numbers.

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