CUBES - Perfect Cubes

For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation a^3 = b^3 + c^3 + d^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {a,b,c,d} which satisfy this equation for a <= 100.

The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.

Note that the programmer will need to be concerned with an efficient implementation. The official time limit for this problem is 2 minutes, and it is indeed possible to write a solution to this problem which executes in under 2 minutes on a 33 MHz 80386 machine. Due to the distributed nature of the contest in this region, judges have been instructed to make the official time limit at their site the greater of 2 minutes or twice the time taken by the judge's solution on the machine being used to judge this problem.

The first part of the output is shown here:

Cube = 6, Triple = (3,4,5)
Cube = 12, Triple = (6,8,10)
Cube = 18, Triple = (2,12,16)
Cube = 18, Triple = (9,12,15)
Cube = 19, Triple = (3,10,18)
Cube = 20, Triple = (7,14,17)
Cube = 24, Triple = (12,16,20)

Added by:Wanderley Guimarăes
Date:2006-06-01
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Mid Central Regionals 1995

hide comments
2014-08-06 13:35:21 Tanmay Sinha
is there any other method apart from brute force???
2013-06-21 18:22:18 Priyanshu
My 100th classical..!!! :D
Yay..!!! :D
2013-05-20 19:48:28 mridul
Code Deleted!
whats wrong with this code?
Ans(Tjandra): Your code is overloop, it print outranged solution. Also don't post any source-code here. For more discussion (hints, ideas, solutions) please visit forum.

Last edit: 2013-05-20 20:17:28
2013-01-02 23:55:00 Muhammad Ichsan Abdillah
i've got the same problem as abby, and the spelling of Cube ama Triple is correct, why?
2012-12-30 13:24:07 viraj
@Abby check the spelling of Cube and Triple in the output. I made a silly mistake there.
2012-07-11 09:14:18 Abby
Need help. Getting the correct output, at least from the first 7 sample outputs. And I'm still getting Wrong Answer. Any ideas?
2011-12-15 12:13:39 ASK
@aman kumar as we have to find integers greater than 1 that satisfy the "Perfect cubes"
2011-12-14 15:07:09 Aman Kumar
Cube = 9, Triple = (1,6,8)
is not in the output ! strange..
2011-12-10 21:12:24 Ankit Paharia
@~
its clearly mentioned a<=100....... how the sum of the cubes of three numbers be greater than 100.......
b,c,d will always be less than 100
2011-06-07 14:19:46 ~
is the given limit that a<=100 should be for b,c,d also??
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