Question 8
A finite sequence of 0s and 1s has the following properties: (1) for any $i \lt j$, the sequences of length 5 beginning at position $i$ and position $j$ are different; (2) if you add an additional digit at either the start or end of the sequence, then (1) no longer holds. Prove that the first 4 digits of the sequence are the same as the last 4 digits.