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5. Coins. 2/4/4 Suppose we place n coins in a circle where n is odd. You are allowed to take two consecutive coins, which either both have heads facing up or both have tails facing up, and flip them over. You can do this operation as many times as desired. Prove that it is possible to reach a configuration where all the coins face the same way after a finite number of operations. 1. How does the number of maximally contiguous groups of heads h compare with the number of such groups t for tails? (Answer should be a statement involving h and t. Answer only will be graded.) 2. Show that at least one group of maximally contiguous heads or tails is even in length. 3. Give a proof that you can reach a configuration where all coins face the same way