Triangle Bisectors
Let’s start with a right triangle with a height of 1 unit and consider two ways of dividing it into two triangles.
Triangle Average Divider
Let’s say instead of “bisecting” the triangle, we draw a line from the top vertex to the base with a length that is the average of the remaining two sides...
Cube Solids
For all questions in this problem, let’s ignore the effects of gravity, which means higher unit cubes can float in space without lower unit cubes to support them.
Flattening Cubes
We want to flatten the outer shell of a cube without tearing or stretching the surface.
Complete Scrambles
Consider trying to scramble a string of numbers, say 1, 2, 3, 4, 5, but with the requirement that none of the numbers can end up where they started. Let’s define this as a complete scramble.
Square in Lattice
Consider drawing squares using the lattice points in a grid as vertices.
Tiling with Tetrominoes
Let’s consider tiling square grids with tetrominoes. Pieces can be rotated, reflected, and repeated as needed.
Symmetry of Polynominoes
Polynominoes are figures made up of square units connected by edges.
Perimeters of Polynominoes
If we separate all tetrominoes according to their perimeters, we would have two groups.
Tiling with Polynominoes
Let’s consider tiling square grids using polynominoes of any number of units.