The respective length, breadth and height of the rectangular cuboid R₁ is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R₂ is A, B and C.

It is known that:

(i) The volume of R₁ is precisely twice that of R₂, and:
(ii) Each of A, B and C is a positive integer with A ≤ B ≤ C

Determine the maximum value of C.

I started by trying to find solutions with c=1 and c=2 (there are none).
When c=3 the equation becomes
(A+2)(B+2)*5=2AB*3
or
B - (10A+20)/(A-10)
the first solution is A=11, B=130, C=3

Then I realized that due to the symmetry of this situation there is a solution when C=130.
Then I realized that the other two values are minimized and the third is maximized.

So the maximum value of C is 130.

(Does this reasoning work?)

Posted by Jer on 2014-11-05 22:36:58