Project Euler 25 Mystery Cache

Acknowledgements

This cache was inspired by Project Euler.

General notes

• To solve Project Euler puzzles, you will probably have to write a computer program.
• Many of the containers are small, and contain neither pen nor pencil.
• There are explicit finding notes in each geochecker.

Large Fibonacci numbers

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n−1 + F_n−2,

where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

The Puzzle

The 12^th term, F₁₂, is the first term to contain three digits, and F₂₃₉₀ the first to contain 500.

Let g(n) be the index of the first term to contain n digits, so that g(3) = 12 and g(500) = 2390.

To find this geocache, first calculate

g(2552) + g(2),

and,

g(1530) + g(1).