In this last part you will think about a strategy of mining BitCoins. A Bit Coin miner tries to find so strings attached to original message such that the new message after Hash calculation starts with k zeros. Only the first miner who solves the cryptographic puzzle receives the mining reward and the transaction fees (a) Suppose you have several opponents who have similar computational ability to you, and they all start with x 0 and then try different numbers according to the ordering rule (0,1,2, 3, order to compete against them, what might be you strategy? (b) Suppose you happen to find that there is another smart guy who uses your strategy in a), what should you do? Suppose again that, each time you get a new strategy, some new smart guy enters the game and uses your newly-developed strategy, what will you do? (c) What might be miners' strategies of choosing numbers for trials in equilibrium?