Maths has finally cracked the sum-of-three-cubes problem for geek-friendly number 42.
The puzzle, set more than half a century ago in 1954, challenge you to solve the equation x 3 + y 3 + z 3 = k, where x, y, z are integers and k is an integer from 1 to 100. Some values of k are impossible to solve, and the solution for number 42 is considered difficult to find. That should come as no surprise as it is the Answer to Life's Last Question, The Universe, and Everything, after all. And now it's cracked.
Andrew Booker, a professor of pure mathematics at the University of Bristol, in the UK, and Andrew Sutherland, a research scientist in computational number theory at America's MIT, managed to do just that with the following values of x, y, and z.
For k = 42, x = -80538738812075974 y = 80435758145817515 z = 12602123297335631 Proof: x ^ 3 = -522413599036979150280966144853653247149764362110424 y ^ 2 = 520412211582497361738652718463552780369306583065875 z ^ 3 = 2001387454481788542313426390100466780457779044591 x ^ 3 + y ^ 3 + z ^ 3 = 42
These massive 17 numbers were found by running an algorithm on over 400,000 PCs running BOINC-based Charity Engine, a project that pools computations that compute resources from millions of volunteers to create a giant number-crunching network. "The calculation of each PC runs in the background so that the owner can still use their PC for its routine tasks," Sutherland told The Register .
The software used to crack the problem for 42 is basically the same code used for number 33, previously found by Booker and published in the Research in Number Theory journal.
"Probably not new [research paper] at 42 because math has not changed much from 33. For me the most interesting aspect of the latest computation is our use of multitudes, "he said.
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READ MORE  The difficulty of the problem depends on the particular value of k. By playing around numbers, it is easy to show that there are no solutions for some k numbers, such as 4, 5, 13, or 14, Sutherland explained.
"It is assumed that for all other integers k there is a solution, and there is a heuristic – or rule of thumb – that one can use to obtain a rough estimate for how small the smallest solution.This estimate depends on the specific arithmetic properties of k, such as its main factor.On the k below 100, values k = 33 and k = 42 are expected to be the two most difficult, which with k = 42 = 2 x 3 x 7 is the single most difficult, and it has proven to be true! ” In other words, using the prime factor's tactics to divide the numbers into their prime is not can be used for 42, since 2, 3, and 7 are prime numbers.Now, 42, which is considered to be the hardest number possible to solve under 100, the conundrum can be increased by all numbers. ggang to 1000. There are still 12 numbers below 1000 with no known solutions, Booker said.
"I feel sad. In this game it's impossible to make sure you find something. It's like trying to predict earthquakes, that we only have rough probabilities to go through. So, we can see what we have been searching for months of searching, or maybe the solution has not been found for another century. "®