MathDB

Six free cells are given in a row. Players

A

and

B

alternately write digits from

0

9

in empty cells, with

A

starting. When all the cells are filled, one considers the obtained six-digit number

z

. Player

B

wins if

z

is divisible by a given natural number

n

, and loses otherwise. For which values of

n

not exceeding

20

can

B

win independently of his opponent’s moves?

Problem Statement