Nim

A Maths Starter of The Day

Pens and pencilsThis is a game for two players.

Make a pile of ten items. Pens and pencils would be suitable.

Each player takes it in turn to remove one, two or three items.

The player to remove the last item is the winner.

Play the game four or five times then write down any strategies you may have found.

Are you good enough to challenge the computer at this game?

 

 

Here's the computer version:



Open in full window: 10 pencils | 11 pencils | 12 pencils | 13 pencils

 

 

 

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Topics: Starter | Arithmetic | Game | Problem Solving

  • Wikepedia,
  • Saturday, February 17, 2007
  • "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."
  • Hannah Maxfield, 9T (St Margaret Ward)
  • Wednesday, March 14, 2007
  • "I found this settler very good because it was practical. The 1st person to remove the third item wins!!!! You can also do this by words"
  • Mere, Kogarah
  • Sunday, March 09, 2008
  • "This is a very cool game, I played it with my sister"
  • Zara, Belmont Academy
  • Wednesday, March 19, 2008
  • "Very interesting...
    Tried it with my sister, mum and friend. Would like to see more practical things though. But overall, very good."
  • Mrs Sweeney's P6/7 Maths Group, Netherlee PS
  • Thursday, March 19, 2009
  • "A great game. What started as a quick starter developed into lots of problem solving. We tried increasing the number of objects, increasing the number of players and increasing the number of objects you could take in one go - 1, 2, 3 or 4. We had lots of fun coming up with strategies, seeing if changing something changed the strategy, and most importantly - seeing if we could beat the teacher!"

    •  

  • Anthony Clohesy, TheChalkface.net
  • Thursday, April 16, 2009
  • "If you wanted to play with the whole class, or have soneone challenge the computer, I've made an excel version of the game - http://www.thechalkface.net/excel/nim.xls
    The rules are slightly different - you can choose to take either 1 or 2 (meaning that you win if you can leave the other person with 1, 4, 7, 10, ... (3n-2) objects)
    The level of difficulty can be altered before or during a game, ranging from random to optimal strategy, and the layout of the objects is designed to aid visual learners in detecting the winning strategy."
  • Karen, Klynnjansen@gmail.com
  • Saturday, February 04, 2012
  • "I absolutely love many of your problems. I search for open-ended ones & your site usually provides a lot of them! Thanks!
    One suggestion I have is to always have one matching a holiday. I really enjoy incorporating the holidays/current events. I see you have a great upcoming one for Valentine's Day. You provided a fun one on Halloween.
    A few that I would like to see added:
    a Mardi Gras week or at least one on Fat Tuesday
    Super Bowl
    100th Day (or related to the number 100, I realize this varies from school to school, but maybe a week's worth of questions geared toward this celebration)
    St. Patrick's Day
    Keep up the excellent problems for our students.
    Greatly appreciated!
    Veterans Day."

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This starter has scored a mean of 4.0 out of 5 based on 127 votes.

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Laptops In Lessons

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

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

Laptops In Lessons

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

Transum.org/go/?Start=March14

Here's the URL which will take students
to "23 0r Bust" and other strategy games based on similar principles.

www.transum.org/go/?to=23

 

Students might also like to try Calculator Nim