Unlocked, Secrets of 42

 The Daily mail had the following article written by Colin Fernandez their  Science Correspondent  in the edition for  9th Sep 2019:-

The number 42 is, famously, the answer to the question of life, the universe and everything in the Hitchhikers’ Guide To The Galaxy.
But while the late author Douglas Adams always insisted he chose the number at random for his science fiction novel series, 42 has actually been perplexing mathematicians for decades.
Until now, it remained the last elusive link in a maths problem known as the Diophantine equation.
The question perplexing mathematicians was this: Can you make all the numbers up to 100 from the sum of three cubes? This is expressed, in mathematical notation, as k = x(cubed) + y(cubed) + z(cubed).
Named after Diophantus, the Greek father of algebra, the original problem was set in 1954 at Cambridge University.
Some numbers are easy – for example, the number 29 can be written as 3³ + 1³ + 1³ (27 + 1 + 1). Others, for instance 4, 5, 13 and 14, have been proven to have no solution.
But 42 had remained elusive, with neither a solution nor proof that it has no solution.
Now a team led by the University of Bristol and Massachusetts Institute of Technology (MIT) have cracked it. Professor Andrew Booker enlisted the help of MIT maths professor Andrew Sutherland, and they used Charity Engine – which uses power from more than 500,000 home computers while they are lying idle.
The answer, which took over a million hours of calculating to prove, is as follows: X = -80538738812075974, Y = 80435758145817515 and Z = 12602123297335631.
Professor Booker, of the University of Bristol, said: ‘I feel relieved. In this game it’s impossible to be sure that you’ll find something. It’s a bit like trying to predict earthquakes. So, we might find what we’re looking for with a few months of searching, or it might be that the solution isn’t found for another century.’
In the Hitchhikers Guide To The Galaxy saga, a group of hyperintelligent beings demand to know the ‘ answer to the Ultimate Question of Life, The Universe and Everything’ from a super computer, Deep Thought. After 7.5million years, it reveals the answer is 42.
While many fans have theorised about the significance of the number 42, the author himself said ‘it was a joke’. Mr Adams, who died in 2001 at the age of 49, said: ‘It had to be a number, an ordinary, smallish number, and I chose that.

The connection between 42 and Lewis Carroll are well known Here are a  three for you:-
The seventh stanza of The Hunting of the Snark has.

 He had forty-two boxes, all carefully packed,
   With his name painted clearly on each:
But, since he omitted to mention the fact,
   They were all left behind on the beach.

Chapter 11 of Alice’s Adventures in Wonderland - Alice’s Evidence contains this line:-
Rule 42. All persons more than a mile high to leave court.

The sixteenth stanza of Canto I of Phatasmogoria is:

“No doubt,” said I, “they settled who
      Was fittest to be sent
Yet still to choose a brat like you,
To haunt a man of forty-two,
      Was no great compliment!”