# 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.

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