# Fibonacci Nim: The Game

Discussion in 'Off Topic' started by it'ship2b^2, Feb 17, 2011.  |  Print Topic

1. Original Member

### it'ship2b^2Silver Member

Messages:
178
317
Status Points:
305
Here are the rules:

1) Start with any number of sticks, chips, or pennies which is not a Fibonacci number. (a Fibonacci number follows the pattern: F(1)=0, F(2)=1, and F(n)=F(n-1)+F(n-2) so each term is the sum of the previous two numbers).
2) The first person takes any number of sticks/chips/pennies away.
3) The next person can take any number of sticks/chips/pennies between 1 and twice the number that the last player took.
4) Repeat (3) until there are no sticks/chips/pennies remaining. The person to take the last stick is the winner.
5) The winner picks the new number and the game begins again.

I take 2 which leaves 48 sticks.

2. Original Member

### SoFlyOnSilver Member

Messages:
1,167
972
Status Points:
895
I take 3 which leaves 45 sticks.

it'ship2b^2 likes this.
3. Original Member

### it'ship2b^2Silver Member

Messages:
178
317
Status Points:
305
I take 5 which leave 40.

4. Original Member

### SoFlyOnSilver Member

Messages:
1,167
972
Status Points:
895
I take 9 which leaves 31

5. Original Member

### it'ship2b^2Silver Member

Messages:
178
317
Status Points:
305
I take 4 which leaves 27.

6. Original Member

Messages:
1,167