NIM – Strategy, Mathematical Game



NIM – Strategy, Mathematical Game



Normal Rules:

1. The object is to NOT take the last match.

2. You may take any amount of matches from any one row. You may not take form more than one row.

3. Once you have taken your match(es), play alternates to your opponent. Continue until someone takes the last match.

Misere NIM

Same rules except whoever takes the last match wins.

NIM – Strategy, Mathematical Game - Parental Involvement Homework

1. Play the game against your parent or guardian at least 5 times and record the winner.

Use the strategies discussed in class when playing the game. Take your time.

2. Explain to your parent(s) / guardian(s) how to count in base 2. Have your parents write the numbers 1-

7 in base 2.

3. Explain to your parents how you can win the game.

4. Draw two different examples of formations that have a Nim value of 0. Show your work.

5. What would your next move be in the following situations? Show the current Nim Values.

a. b.

6. Play against the computer and bring to me a printout of the screen

showing you beat the computer.



7. My child has played the game with me, taught me how to count in Base

2, explained to me how to win, has beat the computer, and we have

worked together to find the answers to problems 4 and 5.

Parent Signature:_________________________________________________________Date:__________

Student Signature:________________________________________________________Date:__________

Normal Nim Strategy:

Learning Targets:

• Understand how to count in Base 2

• Use a Base 2 strategy to beat/solve the Nim Game

1. Binary Numbers (Base 2): The only numbers we can use are:______________

2.

3. Count the # of matches in each row in base 2.

4. Add the columns of numbers up ignoring any

carrying. (if there are an Odd # of 1’s the answer is 1,

if there are an Even # of 1’s the answer is 0.)

5. Your Nim Value is your answer to the columns added up.

6. If you can continually create a Nim Value of 0, your

opponent cannot win.

Examples:

Cheat Sheet:

[pic]

Verify one example for each row to show it has a NIM Values of 0.

4 - Rows

Drawing:

3 - Rows

Drawing:

2 - Rows

Drawing:

Summary: a. To Win, I need to continually:_______________________________________________.

b. In Normal NIM, you cannot lose if you go:________________

c. If I go first, can I still win? If so, how?

-----------------------

[pic]

[pic]

[pic]

NIM Value:_________

Next Move:

Next Move:

Next Move:

Next Move:

Next Move:

Next Move:

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