Sum of Cubes
Math brain teasers require computations to solve.
What is the smallest number that is the sum of two different pairs of cubes?
HintCubic inches in a cubic foot might help.
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Answer
1729.
1 cubed + 12 cubed = 1 + 12x12x12 = 1+1728=1729
10 cubed + 9 cubed = 10x10x10 +9x9x9 = 1000 + 729 = 1729
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Comments
lessthanjake789
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 dullnumbered 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 worldfamous mathguys. 
cms271828
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. 
keosborne
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!!! 
calmsavior
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!

lexymo
Apr 28, 2006
 I hate math!!!!! 
AwwwSweet
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. 
lessthanjake789
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? 
javaguru
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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