Project Euler 17 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.

Number letter counts

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.

The Puzzle

Denote the number of letters in the first n numbers as S(n), so that S(5) = 19. You might also care to verify that S(300) = 5,168 and S(3,000) = 85,946.

To find this geocache, calculate S(6785), and S(6840) ÷ 27.