Project Euler 15 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.

Lattice Paths

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

The Puzzle

You can assume that the coordinates of this geocache are N 52 12.xxx E 0 7.xxx.

If you repeat the calculation above on a 1000×1000 grid, you'll find many more paths. This number begins 204, ends 120, and the middle three digits are 851.

To find the missing numbers calculate how many similar paths there are in 2562×2562 and 4532x4532 grids, and extract the middle three digits of those big numbers.

In May 2025 the cache moved. To the coordinates above subtract 0.044 from the Northings and add 0.013 to the Eastings.