Problem 1: Birthday paradox . The main class is given . The paradox fails
while using the random number generated numbers . Why? Because a random number
generator generates pure random number while the paradox succeeds since the
birthdays are genrally bunched together in few months (society concepts and
such stuffs here!!).

class birth1
{

public static void f ( int n )
{
int exp=0,flag=0,itr=0,i,j;
int [] a= new int[100];
 do{
  for(i=0;i<n;i++)
   a[i]=(int)(Math.random()*365+1);
        //printf("%d  ",a[i]);
   //printf("\n");
   flag=0;
   for(i=0;i<n-1;i++){
      for(j=i+1;j<n;j++)
         if(a[i]==a[j]){
                 flag=1;
                exp++;
        //printf("exp %d, no %d ",exp,a[i]);
         //getchar();
                 break;
         }
      if(flag==1)
         break;
    }
 }while(++itr<10);
 System.out.println(" n = " + n + " exp = " + exp );
 //printf("\n n=%d  experiments=%d \n",n,exp);
    //getchar();
}

public static String getdate( int n)                          //function to convert random numbers into  dates
{
String s = new String();
int [] months= { 31 ,28,31,30,31,30,31,31,30,31,30,31};
for(int i=0;i<12;i++){
    int temp=n-months[i];
    if(temp>0) 
    {
    n=n-months[i];
    continue;
    }
   s=n + " / " + (i+1);
   //return s;
   break;
   }
   return s;
   }
   



Problem 2: Matrix multiplication for real numbers. 

class matrix
    {
       public static double [ ][ ] multiply( double [ ][ ] a, double [ ][ ] b )
        {
            int n = a.length;
            double [ ][ ] c = new double [ n ][ n ];
            for( int i = 0; i < n; i++ )    // Initialization
                   for( int j = 0; j < n; j++ )
                        c[ i ][ j ] = 0.0;
           for( int i = 0; i < n; i++ )
                   for( int j = 0; j < n; j++ )
                        for( int k = 0; k < n; k++ )
                        c[ i ][ j ] += a[ i ][ k ] * b[ k ][ j ];
           return c;
        }

       public static double [][] randomisation(double [][] a)
       {
	int n=a.length;
	for (int i=0;i<n;i++)
	for(int j=0;j<n;j++)
	a[i][j]=(double)(Math.random()*10.0 + 1.0);

	return a;
	}
	
	public static void printmatrix(double [][] x)
	{
	int n=x.length;
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)
		{
		System.out.print("\t"+x[i][j]);
		if((j%(n))==0) System.out.println();
	}
	}
	System.out.println("\n");
	}
}