Suppose,we have two numbers x and y. we can make operations between the numbers, ** Swap the digits between the numbers positions. we want to maximize the multiplication of them.** If we want to maximize the multiplication product between them,then the difference between the two numbers as minimum as possible. suppose,the numbers are 347 and 489 then we have to minimize 489 and maximize 347 without changing the first digits. let's evaluate 347 489 ------->the difference is=142 ------------------------------------- 169683 After that,if we evaluate the numbers with respect to the defining steps:

3
           4

-------------------------------------- 38 44 -------------------------------------- 389 447 ------->the difference is=58 -------------------------------------- 173883 Proved