4 ms·
For a^3 + b^3 + c^3 = 42, You can enumerate a,b pairs and then you need to check whether the "locked in" value of c^3 is a cube. However imagine it takes 1ns
by nserrino 7y ago
For a^3 + b^3 + c^3 = 42,
You can enumerate a,b pairs and then you need to check whether the "locked in" value of c^3 is a cube.
However imagine it takes 1ns to validate a given pair [a,b].
The eventual solution was [-80538738812075974, 80435758145817515, 12602123297335631].
Since no combination of 3 positive (and therefore small) numbers has worked, we know that one of a,b,c are negative. Let's assume at least one of a,b are negative since it doesn't matter how we allocate them.
To reach the final pair of a = 80435758145817515 (the smaller positive integer) and b = -80538738812075974, you have to increment "a" (starting from 0) 80435758145817515 times and decrement "b" (starting from 0) 80538738812075974 times.
That is 80538738812075974*80435758145817515 possible combinations.
Let's assume each one takes 1 ns (which I believe is fairly optimistic at least for a single machine)
That results in a runtime of 6.5e+24 seconds, aka 2.1e+17 years. No matter how many machines you add, the brute force approach does not appear to be feasible.
I am interested to learn more about how they solved it if not brute force.
- jychang 7y ago> I am interested to learn more about how they solved it if not brute force. https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf
- chrisau 7y ago> I am interested to learn more about how they solved it if not brute force. "Professors Booker and Sutherland's solution for 42 would be found by using Charity Engine; a 'worldwide computer' that harnesses idle, unused computing power from over 500,000 home PCs to create a crowd-sourced, super-green platform made entirely from otherwise wasted capacity." https://phys.org/news/2019-09-sum-cubes-solvedusing-real-life.html https://phys.org/news/2019-09-sum-cubes-solvedusing-real-lif...
- MertsA 7y ago>SUSTAINABLE, ULTRA-LOW CARBON - using PCs that already exist but are just underused Wow, do they honestly believe their own marketing nonsense? There's no way the PUE and power efficiency of a bunch of old random desktop computers is going to come close to beating a modern Amazon, Google, or Microsoft datacenter. Cost wise, yeah sure, I'd bet it would be cheaper even with the lower efficiency and increased power usage but as far as "super-green" and low emissions this is just absurd. I think they might honestly not know that idle power usage is a small fraction of full load usage for any modern processor.
- CharityEngine 7y agoWe don't need the datacenters at all. That's the difference. No facilities. No hardware. No bricks, mortar, shipping, mining of metals or rare earths. No replacing of millions of obsolete machines every three years. We tread lighter than any datacenter owner can ever dream of
- scorpion032 7y agoHere: https://www.youtube.com/watch?v=ASoz_NuIvP0 https://www.youtube.com/watch?v=ASoz_NuIvP0 I just came out watching the solution to how he actually solved it.