1. Consider the following game of TAKE-1-4: starting with a pile of 12 coins, two players take turns removing either 1 coin or 4 coins from the pile. The player who takes the last coin wins. (a) For each number n from 1 to 12, explain who has the winning strategy in TAKE-1-4 starting from a pile of n coins. In the cases in which the first player has the winning strategy, state how many coins (1 or 4, or either) the first player should take. (b) Generalize the above by explaining, clearly and precisely, who has the winning strategy in TAKE- 1-4 starting from a pile of n coins for an arbitrary n. [10 marks]