My 10-year-old son introduced me to the following variation on nim.
Instead of allowing the players to take any number of counters from a
pile on a turn, the counters in each pile are arranged linearly, and
then you can only remove A CONTIGUOUS BLOCK of counters. Here
contiguous means no empty spaces, too. I am also talking about normal
play, not misere play here, so that the person who takes the last block
and empties the piles, wins.
I don't know a general strategy for this game. Does anyone know if it
has been studied?
In the particular case he plays with his friend, the initial
configuration looks like:
Pile 1: 1
Pile 2: 2 3
Pile 3: 4 5 6
Pile 4: 7 8 9 10
where I have numbered the counters for clarity. Pile 1 has 1 counter,
on the first line. Pile 2 has 2 counters, on the second line (2 and 3),
etc. So on a move you could take counters 8 and 9, leaving 7 and 10,
and then on the next move the next player could take 7 or 10 but not
both, since there are empty spaces left between them.
It turns out that in this particular case of 10 counters there is a forced win
for the 1st player, who can take either 7 8 9 10 or 8 9 on his first move.
Any info about this variation?
Best, Jeff Shallit
