You may also like

problem icon

Traffic Lights

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

problem icon

Achi

This game for two players comes from Ghana. However, stones that were marked for this game in the third century AD have been found near Hadrian's Wall in Northern England.

problem icon

Jumping Reindeer

A game for 1 person to develop stategy and shape and space awareness. 12 counters are placed on a board. Counters are removed one at a time. The aim is to be left with only 1 counter.

Nim-7

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

A group of children from Manorfield Primary School, Stoney Stanton played this game.

D.H and N.L. said:

To win follow these rules:
If there is one left take it.
For $2$, take both pieces.
If you face $3$ counters and it is your turn you have definitely lost.
If there are $4$ counters left, it is essential to take $1$.
For $5$, take $2$ instead of $1$.

S.W. took these ideas further and came up with some instructions for how to win from the beginning of the game:

The idea of the game is to take the last $1$ or $2$ pieces to win. This ancient game has a theory.

If you go first you can win each time, however when you go second, it depends on what your opponent does for his/her first move.

Go first:
Take $1$ piece, then if your opponent takes $1$ piece, take $2$ pieces to win.
If your opponent takes $2$, (after you took $1$) then take $1$ to win.

Go second: If you go second, then it all depends on what the first person does. If your opponent takes $1$ piece, then you might not win. If your opponent takes $2$, then take $2$ pieces to win.

Well done! I wonder whether anyone can explain why these ideas work?


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.