the explaination goes like this:see the figure the lines vertical lines divide the carom board in a geometry such that the coin goes into the hole.It is a geometric fact that the board should be divided into the parts so that the coin goes into the hole.As the lenght of the board ois 4ft..:half of it will be 2ft and the division into three will be 2/3 2/3 and 2/3.horizontally the line divides the board into two.the path of the coin is shown by the slant line (i think u understand it). now by just appying pytahgoras theorem you get, (1)4/32 +42 = (the path from front edge to hole)2 .: the lenght path is (160/9)1/2=4/3x(10)1/2 (2) 22 +22 =(lenght of centre to hole)2 :. lenght of centre to hole is 2x(2)1/2