MathDB

An infinite sequence of digits

1

and

2

is determined by the following two properties:
i) The sequence is built by writing, in some order, blocks

12

and blocks

112.

ii) If each block

12

is replaced by

1

and each block

112

2

, the same sequence is again obtained.
In which position is the hundredth digit

1

? What is the thousandth digit of the sequence?

Problem Statement