A new card game for two players.
Follow-up to the February Game Rules of FEMTO.
Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and knot
Chance plays no part, and each game must end. The only advantage
that either player can possibly have is to start or to play second.
To work out how to win you need to start by analysing the 'end
game', and the losing position to be avoided, and then work back to
earlier moves. What should you do if there are only two piles? If
there are more piles, what happens if you reduce all the piles to
one counter in each?
This is how you gain control of the game. Make a list of the
binary numbers for the number of counters in each pile. Now to have
control of the game you want to make the number of 1's in each
column even. Whatever your opponent does, when you record the new
binary number for the pile that has been changed, there will be an
odd number of 1's in one or more of the columns. You will be able
to make all the 'column sums' even again.
For example if the numbers of counters in the piles are 7, 6, 4
and 1 you get
A good move now is to take 4 counters from the pile of 7 which
makes the number of 1's in each column even.