MathDB

Peter and Paul play the following game. First, Peter chooses some positive integer

a

with the sum of its digits equal to

2012

. Paul wants to determine this number, he knows only that the sum of the digits of Peter’s number is

2012

. On each of his moves Paul chooses a positive integer

x

and Peter tells him the sum of the digits of

|x - a|

. What is the minimal number of moves in which Paul can determine Peter’s number for sure?

Problem Statement