- A box, having the precise shape of a rectangular cuboid, has integer dimensions.
- When each one of the dimensions is increased by 3, the volume of the box trebles.
Determine the largest possible dimension of this box.
clearvars,clc
for a=1:100
for b=a:1000
for c=b:10000
if (a+3)*(b+3)*(c+3)==3*a*b*c
fprintf('%2d %2d %3d %4d %5d\n',a,b,c,a*b*c,(a+3)*(b+3)*(c+3));
end
end
end
end
original
dimensions area new area
2 16 285 9120 27360
2 17 150 5100 15300
2 18 105 3780 11340
2 20 69 2760 8280
2 21 60 2520 7560
2 24 45 2160 6480
2 25 42 2100 6300
2 30 33 1980 5940
3 7 60 1260 3780
3 8 33 792 2376
3 9 24 648 1944
3 12 15 540 1620
4 5 42 840 2520
4 6 21 504 1512
4 7 15 420 1260
5 6 12 360 1080
6 6 9 324 972
The largest possible dimension is 285.
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Posted by Charlie
on 2022-10-02 12:48:42 |
computer solution
