Project Euler 2 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.

The puzzle

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Let's ignore the odd terms to give a new sequence:

2, 8, 34, ...

Define f(n) as the sum of the first n terms of this sequence, so that:

• f(1) = 2,
• f(2) = 2 + 8 = 10,
• f(3) = 2 + 8 + 34 = 44,
• ...
• f(10) = 2 + ... + 832040 = 1089154.

To find this cache, first find the middle digits of f(150), f(516), f(6506), f(14), f(24), and f(3232).