Another Nim activity.
As an adviser/consultant I had this activity at hand(in my head as it does not need counters or pens and pencils)Objective: To be the last person to take away either 3 or 2 or 1 to leave zero
Players: Two or two teams. (when introducing the activity I would always play the "Class" or Group, so I was one team and the class was the other. This of course made it easier for me to win as a class would try numbers at random, with no clear strategy)
How: First player starts by verbalising ("I will take away 1 and leave 20")
Second player takes away 1, 2, or 3 ("I will take away 2 leaving 18)
First player takes away 1, 2, or 3 verbalising and leaving the remainder
Continue until one player takes away 1, 2, or 3 to leave zero
Encourage: The students(and yourself to find a strategy that will allow you to always win.
Does the first player always win?
Does the second player always win?
What is the last number that you must leave to always win?
Adaptation: Start at Zero and be the first to reach 21
Take away a different set of numbers, e.g. 1, 2, 3, or 4?
Please Dont: Share your strategy, encourage the students to come up with their own. This is the basis of Creativity, Investigations, Becoming Stuck and moving through, Problem Solving.
As soon as two players know a strategy then whoever starts will control the game this is whn you use an adaptation.
When I was working in classes and schools as an adviser/consultant/teacher I would often use this activity as by doing it mentally as explained above helps mental agility with students.
At any break time of the next visit there would be queues of students wanting to play against me so that they "could win" It often took a number of days before I came a cross a student who knew the strategy.
Yes: We could show the working on the board, but this takes away the mental aspects and the strategy is much easier to see!
We could use a pile of 21 counters
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