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?