The Lemon Fool

The answer to everything is 42, but did you know that it was solved
Rather a lot of digits...

This sum of three cubes puzzle, first set in 1954 at the University of Cambridge and known as the Diophantine Equation x3+y3+z3=k, challenged mathematicians to find solutions for numbers 1-100. With smaller numbers, this type of equation is easier to solve: for example, 29 could be written as 33 + 13 + 13, while 32 is unsolvable. All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42.

V8

88V8 wrote:The answer to everything is 42, but did you know that it was solved
Rather a lot of digits...

This sum of three cubes puzzle, first set in 1954 at the University of Cambridge and known as the Diophantine Equation x3+y3+z3=k, challenged mathematicians to find solutions for numbers 1-100. With smaller numbers, this type of equation is easier to solve: for example, 29 could be written as 33 + 13 + 13, while 32 is unsolvable. All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42.

V8

I don't think that's right.

Without looking it up, I think 42 is actually the answer the supercomputer came up with was to "The ultimate question, you know, the question of life, the universe and everything".

So this led them to realise although they had the answer to the the ultimate question, you know, the question of life, the universe and everything, they hadn't really defined what the question really was (is). So they designed and built the biggest, most sophisticated computer ever to figure it out. And they called it "The Earth".

Or something along those lines.

88V8 wrote: All were eventually solved, or proved unsolvable, using various techniques and supercomputers, except for two numbers: 33 and 42.

apologies if I am being thick
what happened to 33

pje16 wrote:apologies if I am being thick
what happened to 33

Ask Mr Dirk Gently. As a former student of St. Cedd's College he might have an idea where to find it.

Urbandreamer wrote:

pje16 wrote:apologies if I am being thick
what happened to 33

Ask Mr Dirk Gently. As a former student of St. Cedd's College he might have an idea where to find it.

very cryptic
but google came to help

There is a famous interesting variant:
[from Wikipedia]
1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number:

[GH Hardy: A Mathermatician's Apology] - as related there by CP Snow
[When Hardy was visiting Srinivasa Ramanujan in hospital] "I thought the number of my taxi-cab was 1729. It seemed to me rather a dull number." To which Ramanujan replied: "No, Hardy! No, Hardy. It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways."

[from Wikipedia]
The two different ways are:
1729 = 13 + 123 = 93 + 103

stewamax wrote: [from Wikipedia]
The two different ways are:
1729 = 13 + 123 = 93 + 103

Oh for superscripts which would have aided this ancient brain in understanding your equation

scotia wrote:

stewamax wrote: [from Wikipedia]
The two different ways are:
1729 = 13 + 123 = 93 + 103

Oh for superscripts which would have aided this ancient brain in understanding your equation

1729 = 1³ + 12³ = 9³ + 10³

Hardy's Apology was one of the influences that persuaded me to study Maths for my degree. I'd recommend it to any intelligent young person today!

Not the fascination with numbers shown in the taxicab anecdote, but his beautiful exposition of a couple of Euclid's profound yet easily accessible theorems, and for the vision of Cambridge as he knew it. Of course the latter was gone by my time there, and the irony is that it was precisely the demise of Hardy's (and Snow's) Cambridge that opened it to comprehensive-school oiks like me (it was only in 1960 that they dropped the requirement for Latin)!