Project Euler 12 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.

The Puzzle

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

• 1: 1
• 3: 1,3
• 6: 1,2,3,6
• 10: 1,2,5,10
• 15: 1,3,5,15
• 21: 1,3,7,21
• 28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

Define f(i,j) to be the j^th digit of the first triangular number to have over i divisors, so:

• f(5,2) = 8,
• f(100,3) = 9.

To find this cache, first find:

• f(500,3), f(1000,3), f(1000,4), f(1000,6), f(1000,1), f(1000,2), f(1000,7);
• f(1500,9), f(1500,3), f(1500,5), f(1500,10), f(1500,7).