MathDB

Given a finite sequence of zeros and ones, which has two properties:
a) if in some arbitrary place in the sequence we select five digits in a row and also select five digits in any other place in a row, then these fives will be different (they may overlap); b) if you add any digit to the right of the sequence, then property (a) will no longer hold true.
Prove that the first four digits of our sequence coincide with the last four

Problem Statement