### Brain Teasers

# Sum of Cubes

Math
Math brain teasers require computations to solve.

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

### Hint

Cubic inches in a cubic foot might help.### 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

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.

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.

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!!!

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

yeah i heard that story too

Apr 21, 2006

How about 1 cubed and 0 cubed?

Apr 21, 2006

Okay, I have it:

0^3 + 0^3 = 0

1^3 + -1^3 = 0

Ta dah!

0^3 + 0^3 = 0

1^3 + -1^3 = 0

Ta dah!

I hate math!!!!!

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.

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

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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