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# Work in pairs on the following version of a game called NIM. A nongraphing calculator is needed for each pair.?

36.

Work in pairs on the following version of a game called NIM. A nongraphing calculator is needed for each pair.

A.Player 1 presses 1 and + or 2 and +. 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 1 and 2. Instead of + , use - . 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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