Problem 7 (5 marks). A word w is called square free if it cannot be written as w = uxxv, where x is a nonempty word. For example, the word 0120 is square free, but 01201012 is not square free as it contains xx, where x = 01. Answer each of the following (no explanations required). 1. Find a square free word over the alphabet {0, 1} that is as long as possible. 2. Find a square free word of length 8 over the alphabet {0, 1, 2}. 3. Find the name of the first known researcher who showed that there are infinitely many square free words over the alphabet of three symbols