Tiling with Rods
The original problem asks for a combination of 1x2 and 1x3 rods that can tile a 5x5 square. Tiling problems have a tendency to get complicated quickly, so let’s start small.
Variants of Sudoku
Today let’s explore one of the deviations from the standard sudoku rules that every row, column, and subgrid (excluded so we can generalize to non-perfect-square side lengths) must have exactly one of each number from 1 to n, where n is the side length of the sudoku puzzle. Let’s include the new rule that a valid solution to a sudoku puzzle must also have one of each number in each of its two diagonals.
Mini Sudoku
Sudoku is a one-player game where the player tries to fill the spaces of an nxn grid using numbers 1 to n, where n is a natural number, such that every column and every row contains exactly one of each number.
Numbers of Polycubes
Let’s define polycubes as three dimensional shapes made up of unit cubes connected by shared faces.
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.