MathDB

A group of students play the following game: they are counting one by one from

00

99

taking turns, but instead of every number they only say one of its digits. (The numbers in order are

00

01

02

...

., meaning that one-digit numbers are regarded as two-digit numbers with a first digit

0

.) One way of starting the counting could be for example

0

1

2

0

4

0

6

7

8

9,

1

1

2

1

1

5

6

1

8

1

0

2

etc. When they reach

99

, the counting restarts from

00

. At some point Csongor enters the room and after listening to the counting for a while, he discovers that he is able to tell what number the counting is at. How many digits has Csongor heard at least?

Problem Statement