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.
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...
Constructing an unsolvable setup in a colour sorting game.
The card game Seven is one where players take turn extending the numerical sequences of cards in their respective suits.
Irish Snap is a multiplayer card game using the standard deck of 52 playing cards where each player takes turns laying down one face up card each while counting. I.e. the first person says “ace” while laying down the first card; then the second person says “two” while laying down the next card. This process is repeated until the card that has just been laid down matches the number the person just called. When such a match happens, all players race to slap a hand on top of the pile of cards, and the slowest person has to take the pile into their hand. The first person to empty their hand wins.
Cutting three dimensional shapes and looking at the possible shapes of the cross section.
Each regular polygram has a regular polygon at its center.
Cutting 3D shapes parallel to the base such that the top and bottom resulting portions have the same volume.