Chocolate games that are variants of nim and interesting graphs made by these games.
Takuto Hieda, and
Kwansei Gakuin University (Japan)
We study chocolate games that are variants of a game of Nim. In this
article you can cut the chocolate in 3 directions, and we represent the
chocolates with coordinates
are the maximum times you can cut it in each direction.
satisfy the inequality
for a fixed natural number
the authors discovered a formula for loser' s states of the chocolate. For
=1 the authors made predictions for the formulas for loser' s states, although they have not managed to prove them.
They also present some interesting graphs made by the sets of L states of the chocolate games for
If you are interested in the beauty of mathematics and not in the
theory of mathematics, please read Section 4 (Some interesting graphs).