

LobowolfXXX Inner circle La Famiglia 1192 Posts 
What's the smallest number than can be expressed as the sum of two cubes...in two different ways?!
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." 
magicjohn2278 Special user Isle of Man UK 538 Posts 
.. don't suppose you are going to accept
(1^3)+(2^3)=9 and (2^3)+(1^3)=9 
magicjohn2278 Special user Isle of Man UK 538 Posts 
Quote:
On 20060317 04:38, magicjohn2278 wrote: ...and if not, then 1729... 
Daegs Inner circle USA 4283 Posts 
Zero, in an infinite number of ways.
(2^3) + (2^3) = 0 (3^3) + (3^3) = 0 
TomasB Inner circle Sweden 1143 Posts 
There is no smallest number with that reasoning, Daegs. You can probably come up with a few examples where the result is smaller than Zero.
/Tomas 
Steve Martin Inner circle 1119 Posts 
1^3 + 12^3 and 9^3 + 10^3
= 1729 (apparently) What's the smallest number than can be expressed as the sum of two cubes...in three different ways?!
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein 
magicjohn2278 Special user Isle of Man UK 538 Posts 
Quote:
On 20060317 08:04, Steve Martin wrote: You've GOT to be kidding! 
stanalger Special user St. Louis, MO 996 Posts 
Quote:
On 20060317 08:04, Steve Martin wrote: 87539319 
Steve Martin Inner circle 1119 Posts 
... which, coincidentally, is my phone number.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein 
Daegs Inner circle USA 4283 Posts 
I wouldnt really say negative numbers are "smaller" than zero, quiet the opposite.
Zero is the smallest number, at least imho. 
TomasB Inner circle Sweden 1143 Posts 
Quote:
On 20060317 23:26, Daegs wrote: Expect some trouble when it comes to inequalities, logic and programming. /Tomas 
Daegs Inner circle USA 4283 Posts 
Well certainly 4 < 0 but which is "smaller"?
smaller /larger refers to reality and in reality there is no zero or negative numbers.... which is why I posted what I did. The way I see it (when it comes to smaller/larger), is that negative numbers have a greater magnitude in the opposite direction of positives. Viewing magnitude, I see zero as "smaller" than 1000 for example. ANYWAY, if you look at it that way that less than = smaller, then the answer is negative infinity as you can keep giving it larger and larger negatives to be cubed and added.. All in all a very poorly worded puzzle imho.... 
TomasB Inner circle Sweden 1143 Posts 
The words "smallest number" was probably a hint that he was talking about maths. Zero and negative you of course find in reality. Your teacher probably explained zero as "none" and negative as "owing". Nevertheless the problem poser spoke of "number" and not fruits or animals.
I agree that the wording of the puzzle could have been stricter, but it's easy to reason that "There is no smallest number." is such a boring answer that he must have meant something else. Since I'm not very good with Diophantine problems, did you guys try different solutions or was there some other way of solving this? /Tomas 
LobowolfXXX Inner circle La Famiglia 1192 Posts 
I had 1729 in mind, but interesting theoretical followup you guys had while I was out of town.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." 
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