MathDB

Initially on the blackboard all the integers from

1

2002

inclusive are written in one line and in some order, without repetitions. In each step, the first and second numbers of the line are deleted and the absolute value of the subtraction of the two numbers that have just been deleted is written at the beginning of the line; the other numbers are not modified in that step, and there is a new line that has one less number than the previous step. After completing

2001

steps, only one number remains on the board. Determine all possible values of the number left on the board by varying the order of the

2002

numbers on the initial line (and performing the

2001

steps).

4

Problems(1)