All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Sum of Cubes (Posted on 2013-10-23)
Express each integer between 1 and 1000 as a sum of four cubes of integers (which can be positive, negative, or zero).

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 going further with the computer, but still 14 missing | Comment 3 of 5 |
(In reply to Computer findings, leaving 45 cases for analytic methods by Charlie)

31 of the missing 45 are found by:

DEFDBL A-Z

DIM cube(50)

OPEN "sumcubes extra.txt" FOR OUTPUT AS #2
DATA 31,50,86,95,148,221,239,265,284,291,292,301,310,356,365,373,382,417,428
DATA 437,499,508,564,571,580,589,598,626,634,643,652,724,725,760,769,778
DATA 787,788,879,886,905,913,914,949,967
DIM needed(45)
FOR i = 1 TO 45
READ needed(i)
NEXT

FOR n = 0 TO 50
cube(n) = n * n * n: PRINT n, cube(n)
NEXT
FOR asub = 0 TO 50
FOR bsub = asub TO 50
FOR csub = bsub TO 50
FOR dsub = csub TO 50
FOR a = -cube(asub) TO cube(asub) STEP cube(asub)
FOR b = -cube(bsub) TO cube(bsub) STEP cube(bsub)
FOR c = -cube(csub) TO cube(csub) STEP cube(csub)
FOR d = -cube(dsub) TO cube(dsub) STEP cube(dsub)
tot = a + b + c + d
good = 0
FOR i = 1 TO 45
IF needed(i) = tot THEN good = 1: needed(i) = 0: EXIT FOR
NEXT
IF good THEN
IF tot > 0 AND tot <= 1000 THEN
PRINT USING "#### = ###### + ####### + ####### + #######"; tot; a; b; c; d
PRINT #2, USING "#### = ###### + ####### + ####### + #######"; tot; a; b; c; d
ct = ct + 1
END IF
END IF
IF dsub = 0 THEN EXIT FOR
NEXT
IF csub = 0 THEN EXIT FOR
NEXT
IF bsub = 0 THEN EXIT FOR
NEXT
IF asub = 0 THEN EXIT FOR
NEXT
NEXT
NEXT
NEXT
NEXT
PRINT ct

CLOSE

50 =  24389 +   24389 +   68921 + -117649
86 =   2744 +    2744 +   24389 +  -29791
95 =     -1 +    2744 +    8000 +  -10648
221 =     -1 +    8000 +   42875 +  -50653
239 =     -1 +   -2197 +  -21952 +   24389
291 =   1000 +    1728 +   21952 +  -24389
292 =  -1331 +   -4913 +  -32768 +   39304
301 =     -8 +  -17576 +  -32768 +   50653
310 =      1 +  -17576 +  -32768 +   50653
365 =    125 +   -2197 +  -21952 +   24389
373 =      1 +    6859 +   97336 + -103823
417 =     -8 +   -2744 +  -32768 +   35937
428 =    -64 +   -6859 + -117649 +  125000
437 =   -343 +   -2197 +  -29791 +   32768
499 = -17576 +  -24389 +  -54872 +   97336
508 =   1000 +    6859 +  117649 + -125000
564 =     -1 +    4913 +    4913 +   -9261
589 =     64 +    4096 +   39304 +  -42875
634 =   6859 +    6859 +   29791 +  -42875
643 =   -125 +   21952 +   64000 +  -85184
652 =    343 +  -17576 +  -32768 +   50653
760 =     -8 +   21952 +   64000 +  -85184
769 =      1 +   21952 +   64000 +  -85184
778 =     64 +   -2744 +  -12167 +   15625
788 =      8 +   -2197 +  -29791 +   32768
879 =    -64 +    2744 +   13824 +  -15625
886 =     64 +   -4913 +   -4913 +   10648
905 =    125 +   -2197 +  -29791 +   32768
913 =  -4913 +   -8000 + -103823 +  117649
914 =  -2197 +   -2197 +   -6859 +   12167
967 =   4096 +   21952 +   29791 +  -54872

 Posted by Charlie on 2013-10-23 12:55:41
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information