Fibonacci Nim/Examples/11
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Example of Game of Fibonacci Nim
Let a game of Fibonacci nim between player $\text A$ and player $\text B$ have a starting pile of $11$ counters.
$\text A$ removes $3$ counters, leaving $8$.
$\text B$ may remove up to $6$ counters, and takes $1$, leaving $7$.
$\text A$ may remove $1$ or $2$ counters, and takes $2$, leaving $5$.
$\text B$ may remove up to $4$ counters, and takes $1$, leaving $4$.
$\text A$ may remove $1$ or $2$ counters, and takes $1$, leaving $3$.
$\text B$ must remove either $1$ or $2$ counters, leaving $\text A$ in a position to take all the counters next turn.
$\text A$ wins.
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers: Exercise $37$