Beads in a Bracelet
We have a bracelet made of yellow and green beads, and we want to divide each coloured beads evenly among friends with the least number of cuts.
Nonlinear Arrangements
Here’s an arrangement of the numbers 1 to 4, and what it looks like plotted into a 4x4 grid such that each row corresponds to a number in the arrangement. Notice that the 3 dots on the bottom right form a straight line.
Nonlinear Dots
Here’s a way to put 6 dots into a 3x3 grid such that no 3 dots form a straight line.
Combination Lock
There’s a combination lock with a 3 digit code with no repeated digits, and for each of our attempts to guess the code it tells us the number of correct digits and ones in the correct places.
Separating Numbers
Here’s one way to put a pair of 1s, a pair of 2s, and a pair of 3s in a row such that the pair of 1s have one number between them, the pair of 2s have two numbers between them, and the pair of 3s have three numbers between them:
Jumping Tiles
In the following puzzle, each number indicates the distance (vertically, horizontally, or a combination of both) this tile needs to move. A solution is a rearrangement of all the tiles in the grid that satisfies all the numbers where none of the tiles overlap.
3D Sudoku
Imagine instead of a two dimensional grid, we are now filling a 3D grid made up of nxnxn unit cubes with numbers 1 to n such that every row, column, and depth has exactly one of each number.
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.