Brain Teasers
Sum of Cubes
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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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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