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
![$ \{x, y, z\}$](img1.png)
, where
![$ x,y,z$](img2.png)
are the maximum times you can cut it in each direction.
The coordinates
![$ \{x, y, z\}$](img1.png)
satisfy the inequality
![$ y\leq \lfloor z/k \rfloor$](img3.png)
for a fixed natural number
![$ k$](img4.png)
.
For
![$ k=2$](img5.png)
the authors discovered a formula for loser' s states of the chocolate. For
![$ k$](img4.png)
=1 the authors made predictions for the formulas for loser' s states, although they have not managed to prove them.
They also present some interesting graphs made by the set of L states of the chocolate games for
![$ k = 1,2,3,4,5$](img6.png)
.