Fibonacci follies: suppose you are playing a round of Fibonacci nim with a friend. You start with 15 sticks. You start by removing two sticks; your friend then takes one; you take two; your friend tak

Fibonacci follies: suppose you are playing a round of Fibonacci nim with a friend. You start with 15 sticks. You start by removing two sticks; your friend then takes one; you take two; your friend takes one. What should your next move be? Can you make it without breaking the rules of the game? Did you make a mistake at some point? If so, where?