The respective length, breadth and height of the
rectangular cuboid R
_{1} is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R
_{2} is A, B and C.
It is known that:
(i) The volume of R
_{1} is precisely twice that of R
_{2}, and:
(ii) Each of A, B and C is a positive integer with A ≤ B ≤ C
Determine the maximum value of C.
For tot = 3 To 3000
For a = 1 To tot / 3
For b = a + 1 To (tot  a) / 2
c = tot  a  b
area2 = a * b * c
area1 = (a + 2) * (b + 2) * (c + 2)
If area1 = 2 * area2 Then
Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
DoEvents
End If
Next
Next
Next tot
finds
a b c
6 8 10
6 7 12
5 8 14
4 12 14
5 7 18
4 10 18
4 9 22
5 6 28
4 8 30
3 20 22
3 18 25
3 16 30
3 15 34
3 14 40
4 7 54
3 13 50
3 12 70
3 11 130
The largest c here is 130, and it looks like solutions stop here.

Posted by Charlie
on 20141106 08:19:07 