Project Euler 16 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.

Power digits & sum

2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. Furthermore, the number 27 is hidden (poorly) in these digits.

The Puzzle

2¹⁷⁹⁷³ is a 5411 digit number beginning 25829.

To find this geocache, calculate 2¹⁷⁹⁷³, and find the northing hiding in its digits. You should assume that the northing begins N 52 10.

To calculate the easting, find the difference between the sum of the 3069 digits starting 5210, and the first 1000 digits of the number i.e. (5 + 2 + 1 + 0 + ... ) - (2 + 5 + 8 + 2 + 9 + ... ).