42 is the sum of three cubes

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


This is wonderful news.


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


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

Thanks for the fish


I’m slow, so please help me:
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.


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


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


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

Bother bother bother… :face_with_raised_eyebrow:

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.


But there’s clearly five of them.


I see Zappa back there also. :slightly_smiling_face:


41 is the sum of five dudes…


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


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.
This is where Douglas Adams got his answer, methinks.

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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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