# A Fibonacci Set of Sticks

Geometry Level 3

Recently, I was cleaning up my attic, and I found a set of sticks which, some years ago, a curious Italian gentleman sold me. I was trying to figure out why I bought it from him, and I realized that the set has the incredible property that there are no $$3$$ sticks that can form a triangle. If the set has two sticks of length $$1$$, and these are the smallest, what is the least possible length of the $${ 14 }^\text{th}$$ stick?

Assumptions: My set of sticks has at least 14 sticks.

×