Project Euler 21 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.

Amicable Numbers

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).

If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair, and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

The Puzzle

To find this geocache first calculate the product of all the amicable numbers under 100,000. Denote the n^th digit of this number by d_n.

Now visit N d₃₉d₄₀ d₄₁d₄₂.d₄₄d₃₂d₃₃ E d₆₄ d₇₁.d₈₂d₈₃d₈₈.