The published coordinates are for the Lancaster branch of a well-known optician chain -- you will not find the cache there. However, Leonhard Euler was a Swiss mathematician, physicist, astronomer, logician and engineer. In addition, Euler is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler suffered with eyesight problems for much of his life.
Acknowledgements
This cache was inspired by Project Euler and by a very similar series of caches in Cambridge by mjouk.
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.
- Caches are placed around Lancaster and the surrounding areas. Many of the caches are in busy or residential areas.
There are currently 7 caches in the Lancaster series.
Find them all: 1, 2, 3, 4, 5, 6, 7
The sum of the squares of the first ten natural numbers is 385.
The square of the sum of the first ten natural numbers is 3025.
The difference between these two is 2640.
Define fi(n) to be the first i digits of the difference between the square of the sum of the first n natural numbers and the sum of the squares of the first n natural numbers.
So, f3(10) = 264.
To find this cache, calculate:
- f2(2160)
- f4(5948)
- f1(575)
- f2(2091)
- f3(771)
Project Euler Hall of Fame
For the complete Hall of Fame, visit: http://www.sclinch.com/geocaching/euler.html