Mathematics
Starting with a square, choose two points on the perimeter of the square to make a line, and then move both end points incrementally in the same direction (clockwise or counterclockwise) and the same distance along the perimeter of the square to make subsequent lines.
In a game of Peg Solitaire, 32 pegs are arranged in a cross shaped grid with the center peg removed. In each move, the player is allowed to move one peg over another, vertically or horizontally onto an empty space, and remove the peg that was jumped over. The game continues until no legal move is available, and the goal is to have as few pegs remaining as possible when the game ends. A perfect game would end with a single peg back in the center of the board.
Tower of Hanoi is a one-player game using three vertical rods and a number of disks, all of different diameters. The goal of the game is to move the entire pile of disks onto one of the other two pegs.
The standard number system we use today is called decimal numbers, or base 10, meaning at every digit, we count to 9 before carrying one to the next smallest digit.
A continued fraction is a way to represent any real number as a sequence of integers by writing down the integer part of the real number and taking the reciprocal of the remaining part at each iteration.
A perfect number is a natural number that is equal to the sum of all of its proper divisors (divisors that are less than the number itself). For example, 6 is the smallest perfect number because its proper divisors, 1, 2, and 3, add up to exactly 6.
Consider all pairs of natural numbers that add to 9, which pair has the largest possible Least Common Multiple?
Triangular numbers and trapezoidal numbers are both natural numbers that can be expressed as the sum of more than one consecutive natural numbers.
Some numbers can be expressed as the sum of two perfect squares...
Sliding numbered blocks in a square grid to put them back in numerical order.