N is the smallest number which can be represented by two different sums of 4 positive (not necessarily distinct) cubes.
Find N and the corresponding sums.
DEFDBL A-Z
OPEN "twoexps.txt" FOR OUTPUT AS #2
FOR a = 1 TO 40
a3 = a * a * a
FOR b = a TO 40
b3 = b * b * b
FOR c = b TO 40
c3 = c * c * c
FOR d = c TO 40
d3 = d * d * d
sum = a3 + b3 + c3 + d3
PRINT #2, USING "#######"; a3; b3; c3; d3; sum
NEXT
NEXT
NEXT
NEXT
CLOSE
The output file is then sorted on the sum column and read by:
OPEN "twoexps.txt" FOR INPUT AS #1
CLS
DO
prev$ = l$
LINE INPUT #1, l$
IF MID$(l$, 30) = MID$(prev$, 30) THEN
PRINT prev$
PRINT l$
PRINT
ct = ct + 1: IF ct > 12 THEN END
END IF
LOOP UNTIL EOF(1)
the result is:
1 1 1 216 219
27 64 64 64 219
1 1 125 125 252
1 8 27 216 252
1 8 125 125 259
8 8 27 216 259
8 27 27 216 278
1 27 125 125 278
1 64 125 125 315
8 27 64 216 315
8 27 125 216 376
1 125 125 125 376
8 27 216 216 467
1 125 125 216 467
27 27 125 343 522
1 1 8 512 522
1 125 125 343 594
8 27 216 343 594
1 64 125 512 702
8 8 343 343 702
1 1 27 729 758
8 64 343 343 758
8 27 216 512 763
1 125 125 512 763
64 64 125 512 765
1 8 27 729 765
so the answer is 219 = 1+1+1+216 = 27+64+64+64.
BTW, eyeballing the output, allowing it to continue past the above, indicates the first instance that would satisfy disallowing repeated cubes within a given sum would result in the following as the lowest:
1 + 8 + 27 + 1000 = 1036
27 + 64 + 216 + 729 = 1036
If you want no repeats whatsoever among the eight cubes, then:
1 + 125 + 512 + 1000 = 1638
27 + 64 + 216 + 1331 = 1638
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Posted by Charlie
on 2011-12-22 14:09:17 |
computer solution (spoiler)
