Tiling with Polynominoes
Let’s consider tiling square grids using polynominoes of any number of units.
Perimeters of Polynominoes
If we separate all tetrominoes according to their perimeters, we would have two groups.
Symmetry of Polynominoes
Polynominoes are figures made up of square units connected by edges.
Tiling with Tetrominoes
Let’s consider tiling square grids with tetrominoes. Pieces can be rotated, reflected, and repeated as needed.
Square in Lattice
Consider drawing squares using the lattice points in a grid as vertices.
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.
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.
Covering Squares
We choose one space in a rectangular grid made of unit squares, and we count the number of squares or rectangles that cover this space.
Counting Rectangles Extended
Continuing from last week’s problem about counting squares, let’s look at the related problem of counting the number of rectangles in a grid, with extensions
Counting Squares Extended
Consider the widely known problem of counting the number of squares in a square grid. Today we will try to extend the problem.