**Shunsuke Nakamura,**

**Daisuke Minematsu,**

**Takeru Kitagawa,**

**Youichiro Naito,**

**Ryohei Fujii,**

**Takuto Hieda, and**

** Ryohei Miyadera
**

**Kwansei Gakuin University (Japan)
**

**(runners@kwansei.ac.jp)**

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
, where
are the maximum times you can cut it in each direction.
The coordinates
satisfy the inequality
for a fixed natural number
.
For
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).

If you are interested in the beauty of mathematics and not in the theory of mathematics, please read Section 4 (Some interesting graphs).

- Introduction
- A proof of Theorem
- Chocolates without simple formulas for L-state
- Some interesting graphs produced by the set of L states
- Bibliography
- About this document ...