Competitive Programming #14: [Maximize the volume of Cuboid]

Given the sum of length, breadth and height of a cuboid. The task is to find the maximum volume that can be achieved such that the sum of sides is S.
Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains an integer S.
Output:
For each test case, print the maximum volume you can obtain in new line.
Constraints:
1<=T<=500
3<=S<=10⁵
Example:
Input:
2
4
8
Output:
2
18

Explanation:

Input : S = 8
Output : 18
All possible edge dimensions:
[1, 1, 6], volume = 6
[1, 2, 5], volume = 10
[1, 3, 4], volume = 12
[2, 2, 4], volume = 16
[2, 3, 3], volume = 18

Solution:

Lets give our examples:

INPUT: 

3

65
21
31 

1# Sum_Of_Sides = 65; We check if Sum_Of_Sides is divisible by 3.
    No it isn't
    Check if Sum_Of_Sides modul by 3 has remindеr 1.
    No, it hasn't
    So Sum_Of_Sides % 3 = 2 
    print (Sum_Of_Sides➗3 + 1 ) ^2 * (Sum_Of_Sides ➗ 3);

2# Sum_Of_Sides = 21; We check if Sum_Of_Sides is divisible by 3.

      Yes it is: print (Sum_Of_Sides➗3)^3;

3# Sum_Of_Sides = 31;

     31➗ 3 = 10 ; (reminder = 1)
     print  (Sum_Of_Sides➗3)^2 * (Sum_Of_Sides ➗ 3 + 1);

That 'divisible by 3 ' is cause [Breadth, Height, Length]

This problem is mathematics also 😄