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The cube stacking game is a two-player game version of this puzzle. Given an ordered list of cubes, the players take turns adding the next cube to the top of a growing stack of cubes. The loser is the first player to add a cube that causes one of the four sides of the stack to have a color repeated more than once.
The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards dealt and the first player that can achieve the number 24 exactly using only allowed operations (addition, subtraction, multiplication, division, and parentheses) wins the hand.
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A scrambled Rubik's Cube. An algorithm to determine the minimum number of moves to solve Rubik's Cube was published in 1997 by Richard Korf. [10] While it had been known since 1995 that 20 was a lower bound on the number of moves for the solution in the worst case, Tom Rokicki proved in 2010 that no configuration requires more than 20 moves. [11]
A completed game. The 2048 tile is in the bottom-right corner. 2048 is played on a plain 4×4 grid, with numbered tiles that slide when a player moves them using the four arrow keys. [4] The game begins with two tiles already in the grid, having a value of either 2 or 4, and another such tile appears in a random empty space after each turn. [5]
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number, is
Up-and-down elevator games and Piet Hein's mechanical puzzles: 1973 Mar: The calculating rods of John Napier, the eccentric father of the logarithm 1973 Apr: How to turn a chessboard into a computer and to calculate with negabinary numbers 1973 May: A new miscellany of problems, and encores for Race Track, Sim, Chomp and elevators 1973 Jun