MathDB

All

10

-digit numbers consisting of digits

1, 2

and

3

are written one under the other. Each number has one more digit added to the right.

1

2

3

, and it turned out that to the number

111. . . 11

added

1

to the number

222. . . 22

was assigned

2

, and the number

333. . . 33

was assigned

3

. It is known that any two numbers that differ in all ten digits have different digits assigned to them. Prove that the assigned column of numbers matches with one of the ten columns written earlier.

Problem Statement