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a. Player 1 presses 1 2 or 3 . Player 2 does the same. The players take turns until the target number of 21 is reached. The first player to make the display read 21 is the winner. Determine a strategy for deciding who always wins.b. Try a game of NIM using the digits 1 2 3 and 4 with a target number of 104. The first player to reach 104 wins. What is the winning strategy?c. Try a game of NIM using the digits 3 5 and 7 with a target number of 73. The first player to exceed 73 loses. What is the winning strategy?d. Now play Reverse NIM with the keys and instead of 0 put 21 on the display. Let the target number be 0. Determine a strategy for winning Reverse NIM.e. Try Reverse NIM using the digits 1 2 and 3 and starting with 24 on the display. The target number is 0. What is the winning strategy?f. Try Reverse NIM using the digits 3 5 and 7 and starting with 73 on the display. The first player to display a negative number loses. What is the winning strategy?

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