Daniel Kunkle spent most of his time at the College with a colorful puzzle like Rubik’s Cube. And for 20 years, Jonathan Schaeffer, worked to win in checkers.
The two researchers are not Goofing off. Intelligent programming with the computer, Kunkle that a Rubik’s Cube can be solved in 26 moves or less. The previous record was 27 and Schaeffer has shown that if the two opponents in a perfectly Dame game, the game will always be a draw.
Playing games and puzzles is a great way to sharpen your problem-solving skills.
Study of puzzles and games can be fun, but work may also eventually help scientists to solve real problems.
Cracking the Cube
Each side of a Rubik’s cube is divided into nine squares, like a Tic-Tac-Toe board. If the puzzle is solved, all nine squares (called facelets) on each side of the same color as another. There is one side red, one green, and so forth. Facelets hinges allow turn lanes.
When the puzzle is solved, each side of a Rubik's Cube contains squares, or facelets, of just one color.
A number of rotations of colors mixed randomly. To solve the puzzle, you must select the proper number of turns in the group of colors.
The facelets a Rubik’s Cube in about 43 trillion (which is 43 with 18 zeros after) as possible. A hand can take a long time to find a solution.
A computer can try to move and to compare the solutions to solve the problem is much faster. But with so many ways (including configuration), the fastest computer in the world is a ridiculously long time to solve the problem.
To save time, scientists Kunkle and Gene Cooperman from Northeastern University in Boston, Massachusetts, in search of strategies for tackling the problem into smaller parts.
First, it calculates the number of steps would be needed to solve the puzzle with only half a turn, a facelet on the opposite side of the cube. Excluded from the fourth lap, when a facelet ends at the side of the cube in the vicinity, where he started.
Their study showed that only 600,000 possible configurations can be solved in this way. With a desktop computer, Kunkle found that these provisions could be solved in 13 moves or less.
Parties
Subsequently, the researchers wanted to calculate the number of steps to take a different approach of the special arrangements 600,000 presolved. This takes time, more than 1.4 billion search settings. To expedite the process, Kunkle and Cooperman wrote a computer program for a very fast, so-called supercomputers.
A mixed-up Rubik's Cube can take many hours to solve, unless you have the brain of a supercomputer!
He is the supercomputer 63 hours to calculate. The results showed that each configuration can presolved an average configurations in 16 moves back or not. Remember that the maximum number of 13 steps to address these specific settings. In summary, the researchers concluded, the configuration could be solved in a maximum of 29 steps.
The results fell shy of the record 27 passes a year by another researcher. Kunkle and Cooperman said, however, that only about 80 million configurations (much less than 1 percent of all opportunities) really need more than 26 steps to find a solution. Thus, the couple in a few rules.
This time, instead of trying to avoid any difficulties in creating a special configuration, which searches through all possible means to solve each.
The effort was worth it: it has set a new record of 26 steps. The researchers that the absolute minimum is just 20 steps, but still a way to find it.
Strategies, Kunkle and Cooperman for solving the cube can be extended to other complex problems, especially those looking through a lot of possibilities. The schedule of flights of aircraft of millions of people in a variety of ways, as soon as possible, is an example.
Board of Directors of solutions
The solution to the Rubik’s Cube was a great achievement, but Jonathan Schaeffer, University of Alberta in Edmonton, Canada, where an even greater challenge: to win a lady.
The traditional 8-square by 8-square board, each player starts with 12 pieces in three rows back. All measurements are diagonal. In each train, you press one of his pieces at a distance of a space on the side of the opponent.
You can use an enemy piece by jumping on this with one of you in an open space. If one of your opponent’s pieces in hand, deserves the chance to go back. If you can piece all the enemies, you win.
At the beginning of a game of checkers, each player lines up his or her pieces on one side of the board. Players take turns moving a single piece one diagonal space at a time. (This is a special board with 100 squares and 4 rows of pieces per team instead of the usual 64 squares and 3 rows.)
Nobody had ever tried to write a program to simulate all the movements on a chess board. This could be due to the fact that the pieces on a chessboard can be used in more than 500 billion forms (which is 5 with 20 zeros after). Compared to a Rubik’s Cube, a chessboard is 10 times more possible configurations.
Like the Rubik’s researchers, Schaeffer and his colleagues with a small problem. It has two pieces on the board after a game. For each position that both parties can demonstrate a computer program to simulate all possible outcomes.
A game of checkers gets more complicated with each move.
The program has been through the same process of 3 pieces, then 4 and so on, up to 10 pieces. There are currently 39 billion opportunity, where the pieces can be.
Checkmate
Schaeffer added that if a piece on the board, the time needed for the calculations was 10 times greater than the time required for the previous step. The computer is not powerful enough to continue the process.
Schaeffer started right from the start of the game. His program of all possible moves and movements, up just 10 points left on the camera. Since he had already discovered all kinds of game, whether or not 10 pieces left, you could, the two programs to simulate an entire game.
Despite the efforts made by Schaeffer to reduce downtime, the team has 18 years, until the end of the problem. “I am very surprised that I have enough patience to keep up with this,” said Schaeffer.
It took computers 18 years to come up with a solution for the game of checkers. Chess, shown here, is an even more complicated game.
As the methods of Rubik’s Cube Kunkle, Schaeffer strategies may be applied to practical problems in planning and human biology. The work could one day contribute to a perfect team to play a game of chess, which is much more complicated than Dame.
Kunkle Schaeffer games and can lead to serious science.