Project Euler 6 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

The sum of the squares of the first ten natural numbers is 385.

The square of the sum of the first ten natural numbers is 3025.

The difference between these two is 2640.

Define f_i(n) to be the first i digits of the difference between the square of the sum of the first n natural numbers and the sum of the squares of the first n natural numbers.

So, f₃(10) = 264.

To find this cache, first calculate:

• f₂(1201),
• f₂(1415),
• f₃(2215),
• f₁(1),
• f₁(1378),
• f₃(1127).