Project Euler 22 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.

Names scores

The names.txt file contains nearly 6,000 pseudonyms, some of which you might recognize.

Begin by sorting this list into alphabetical order. Then for each name in the list sum the letters in the name, using the usual A = 1, B = 2, … convention. Suppose the sum of the i^th word in the list is a_i. Now calculate:

f = ∑_i i × a_i,

g = ∑_i i²× a_i.

For example, when the list is sorted into alphabetical order, MJOUK, which is worth 13 + 10 + 15 + 21 + 11 = 70, is the 3274^nd name in the list. So, MJOUK contributes 3274 × 70 = 229,180 to f and 3274² × 70 = 750,335,320 to g.

The Puzzle

If f_i is the i^th digit of f, then you can find the cache at:

N f₈f₁ g₃f₂.f₃(g₁/g₂)(g₉/g₁₀) E g₁₁ g₈.g₅g₁₂(f₄-g₁₃).