Calculator Nim





This is a game for two players:

You may use only these keys.

1 2 3 4 5 6 7 8 9 + =

Take turns to add a single-digit number to what is already on the calculator.

The winner is the player who makes the display show 30.

If you go over 30 you lose.


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Topics: Starter | Arithmetic | Calculator | Games | Problem Solving

  • Wikepedia,
  •  
  • Variants of Nim have been played since ancient times. The game is said to have originated in China (it closely resembles the Chinese game of Tsyanshidzi, or "picking stones"), but the origin is uncertain; the earliest European references to Nim are from the beginning of the 16th century. Its current name was coined by Charles L. Bouton of Harvard University, who also developed the complete theory of the game in 1901, but the origins of the name were never fully explained. The name is probably derived from German nimm! meaning "take!", or the obsolete English verb nim of the same meaning. Some people have noted that turning the word NIM upside-down and backwards results in WIN.

    Nim is usually played as a misère game, in which the player to take the last object loses. Nim can also be played as a normal play game, which means that the person who makes the last move (i.e., who takes the last object) wins. This is called normal play because most games follow this convention, even though Nim usually does not.
  • Aaron Joseph, Nlc
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  • This game would be better if it was for one player. It is so easy. if you are player one you can always win. because the most ovibous one is 15 add 15 or 29 add 1 and 20 add 10. its just too easy
  • Josh, King's Gloucester
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  • This is a great introduction to calculator work.

    You cannot just add 15 and 15 as the rules clearly state you can only add single digit numbers!
  • Jeff Locklier, Neerim District Secondary College
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  • Perhaps some method of crossing out the numbers on screen as thety are used in the game.
  • Cameron, Y7
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  • You can always win if you go 2nd because you can get to 10 and they cant beat you 5+5=10 if they choose any other number just make the number bonds to ten,. E.g 1+9, 3+7, 6+4 etc...
  • Transum,
  •  
  • Here is an idea for playing two person games like this with a class. Arrange the desks along three of the outside walls of the classroom in a sort of horseshoe shape. Pupils sit, two to a computer (laptop, iPad etc) to play the game. The teacher starts the game time and each pair plays one game then turns their chairs to face the teacher when they have finished. When everyone has finished the teacher instructs the pupils to move clockwise if they just won the game or anticlockwise if they lost. The pupils at either end of the horseshoe stay where they are. Repeat this many times. The pupils will move towards playing other pupils of similar insight into the strategies of the game and hopefully discover more about the number patterns involved. It is always, yes always in my experience, great fun for all involved.
  • Jake X, Scarborough, Canada
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  • I should always want to be player 2. He/she has a winning strategy. Player one goes first, player two chooses in such a way that the result is 10 this is always possible. Now player one must go again. Starting with 10, the only result is 1119 so player 2 chooses so that his/her result is 20. Now player one is guaranteed to loose.

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This starter has scored a mean of 3.3 out of 5 based on 151 votes.


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Answers


Extension

If the target was 53 instead of 30 what strategy could you use to win?

Investigate for other targets and different available calculator keys.


Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

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Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=November14

Here is the URL which will take them to Multi-pile Nim which is a different game but based on similar principles.

Transum.org/go/?to=Nim

Student Activity

 

You might also like to try Simple Nim with pens and pencils.

 


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