MathDB

Consider the following one-person game: A player starts with score

0

and writes the number

20

on an empty whiteboard. At each step, she may erase any one integer (call it a) and writes two positive integers (call them

b

and

c

) such that

b + c = a

. The player then adds

b\times c

to her score. She repeats the step several times until she ends up with all

1

's on the whiteboard. Then the game is over, and the final score is calculated. Let

M, m

be the maximum and minimum final score that can be possibly obtained respectively. Find

M-m

6