MathDB

The integer numbers from

1

2002

are written in a blackboard in increasing order

1,2,\ldots, 2001,2002

. After that, somebody erases the numbers in the

(3k+1)-th

places i.e.

(1,4,7,\dots)

. After that, the same person erases the numbers in the

(3k+1)-th

positions of the new list (in this case,

2,5,9,\ldots

). This process is repeated until one number remains. What is this number?

Problem Statement