The Math Behind The Perfect Man

This approach is known as the Rule of Product . You can learn more about it by reading the linked page.

 The figure 
                                 O             Face 
                               --|--            Mid
                                 /\             Legs

     1)    When the right hand touch any part of the circle       above the square and left is straight

                            O/                          
                          --|   
                            /\

         2)         When the right hand touch the corner of the square and left is straight
                            O/                          
                          --|
                            /\

         3)          His both the hands are straight                    
                                   O                          
                                 --|--
                                   /\

         4)       When his right hand is lower than the above      case and left is straight
                             O                 
                           --|\        
                             /\

           5)    When the both the hand touch any part of the  circle above the   square             
                            \O/                          
                             |   
                             /\

         6)  When the right hand touch the corner of the square and left touching any part of the circle above the corner of  the  square

                           \O/                          
                            |                       
                            /\

         7)  When his right hand is straight than the above    case and left touching any part of the circle above the square

                              \O                          
                               |--    
                              /\

         8)      When his right hand is lower than the above   case and left touching any part of the circle above the square

                               \O                          
                                |\          
                                /\

Similarly when his left hand at the square corner and below the arm level (as in case 4)

The man has 4 limbs and each limb can be in 2 position's therefore, it can be placed in $4^{2}$ positions, or 16 positions.

why 2 positions??? wil any explain please

4 poit tichs by his arm fingre and 4 is by his limb so totly points are 8

But you are not taking into account the circular symmetry, so is'nt it 16/2=8

ahhh