Divisibility Test

$N=a b c d e$

To be divisible by it should satisfy $(a+c+e)-(b+d)=11 k$

As, $(7+6+5)-(3+4)=11$

So, $k$ can be $0,1$

Case(1) : $k=0$

$a+c+e=b+d$ .These all numbers are in A.P. so sum of three can not be equal to sum of two.

Case(2): $a+c+e-b-d=11$

This has only one solution i.e. $(a,c,e)$ can be $5,6,7$ and $(b,d)$ can be $(3,4)$

Taking permutations of these numbers total number of N is = $3! \times 2!=12$

class MyClass {

public static void main(String[ ] args) {


    for(int a=3;a<=7;a++){


      for(int b=3;b<=7;b++){if (a!=b){


         for(int c=3;c<=7;c++){if(b!=c && a!=c){


             for(int d=3;d<=7;d++){if(c!=d && b!=d){


            for(int e=3;e<=7;e++){if(d!=e && c!=e){


            if(a!=d && a!=e){


           if(b!=e){


String f=Integer.toString(a)+Integer.toString(b)+Integer.toString(c)+Integer.toString(d)+Integer.toString(e);


                  int s=Integer.parseInt(f);



              {if(s%11==0)



              {System.out.println(""+a+b+c+d+e);}}


         } 


        }


  }}}}


 } }


 }}




        }


       }


       }