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Sum of Cubes

Math brain teasers require computations to solve.


Puzzle ID:#29912
Fun:*** (2.28)
Difficulty:*** (2.85)
Submitted By:lessthanjake789*us*****




What is the smallest number that is the sum of two different pairs of cubes?

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1 cubed + 12 cubed = 1 + 12x12x12 = 1+1728=1729
10 cubed + 9 cubed = 10x10x10 +9x9x9 = 1000 + 729 = 1729


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Apr 20, 2006

An interesting story to go along with this is when one famous mathematician, Hardy, when to visit another, Ramanujan while he was sick, Hardy remarked "I came in a particularly dull-numbered cab, 1729." to which Ramanujan immediately replied - 1729 isn't dull, in fact it's quite interesting as it is the first number made by the sum of different pairs of cubes." Other mathematicians have explained this away as not being the remarkable, as "just about anyone" knows 12 cubed is 1728 and 9 cubed is 729, so the rest from there is pretty easy, so the only REAL piece of information was that Ramanujan knew it was the FIRST number at which this occurred. I on the other hand, was baffled by the whole process, so kudos to world-famous math-guys.
Apr 20, 2006

Yep, I've read that story before too, and I knew the answer straight away. I guess you could write a computer program to find it too.
Apr 20, 2006

I don't get it?? I thought it was very easy at first -- 1 cubed times 2 cubed = 9.

Nevertheless - a very interesting story... and a great teaser which still has me thinking!!!
Apr 20, 2006

yeah i heard that story too
(user deleted)
Apr 21, 2006

How about 1 cubed and 0 cubed?
(user deleted)
Apr 21, 2006

Okay, I have it:

0^3 + 0^3 = 0
1^3 + -1^3 = 0

Ta dah!

Apr 28, 2006

I hate math!!!!!
May 26, 2006

Or you could just cube -1 and -12, -10 and -9. Obviously this could continue for an infinity (AGH!!) so I suppose the numbers should be limited to whole numbers.
Jun 03, 2006

ok, i shall quantify it as counting numbers, terefore excluding negatives and zero, making my solution the first - that sound alright to everyone?
Jan 16, 2009

I sort of remembered the answer used 1^3, but didn't remeber the rest (although 5^3 kept nagging at me). Just to punish myself for forgetting the answer I worked it out by hand...took about 10 minutes.

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