in case you were wondering, i'm a geo main

2012 AMC 10B #25

A bug travels from A to B along the segments in the hexagonal lattice pictured above. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?

To solve this, we can split the diagram into 5 sectors, knowing that each arrow not filled in is "restricted" in a way. I drew vertical partitions along the arrow verticals that were only filled, and found the path possibilities for each section in turn. After connecting each sector based on the answers I recieved, the problem resulted in an answer of 2400. This one was strangely similar to a programming question.

2011 AMC 10B #24-#25

Though I can't seem to get the file onto the page, these two questions were very interesting, #24 being about rays on the Cartesian plane, #25 being about triangle sequences, each triangle a step down with side lengths at the tangent points of the triangle to its incircle . . .

2011 AMC 10B #22

A pyramid has a square base with sides of length 1 and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the faces of the pyramid. What's the cube volume? This was interesting. 3-dimensional geo is fascinating to visualize. It took many steps to end up with simple Pythagorean Theorems, but in the end, the answer was determined.