Now that the first layer is complete, turn the cube over so that the white layer is facing down. If the corner piece is in the top layer, do the following sequence to move it down into the bottom layer: R’ D’ R 3) The Middle Layer Times until it is in the correct position: R’ D’ R D With the corner piece in this position, do this sequence multiple If a corner piece is already in the bottom layer, rotate the bottom layer until it is directly below where it should go like the images below. Hold the cube with the white cross facing up. Many will be able to figure out the white cross with no instruction, but you can go to the video version of the instructions if you find yourself stuck. The completed white cross should look like the picture below.įor this first step, spend some time playing with the cube and get a feel for how the pieces move. This step takes a little work and practice to figure out. Find each of the white edges and get these into position so that the white sticker is on top with the white centerpiece and the side stickers match with the side centerpieces. The first step in solving the cube is to build the white cross. Letter followed by the number 2 indicates doing the move twice. To be informed about new articles on I Programmer, sign up for our weekly newsletter, subscribe to the RSS feed and follow us on Twitter, Facebook or Linkedin.An explanation of cubing notation: In these instructions and with almost all cubing guides, we will use cubing notation.Īre the equivalent moves counter-clockwise Solving the Rubik's Cube Optimally is NP-complete Related Articles Unless P=NP, it looks increasingly likely that we will never know God's number fo anything other than a 3x3x3 cube. So answering the question of whether a particular cube can be solved in n moves is NP complete and hence NP hard. The key to proving this is to show that the problem is the same as finding a route that visits the nodes of a particular graph just once, a Hamiltonian Cycle - and this problem is known to be NP complete. In fact it is an NP complete problem, which means if you can find a polynomial solution for it then you have found a solution for all problems in NP and you have proved that NP=P, which would earn you the million dollar prize from the Clay Mathematics Institute - not to mention fame and fortune and the key to all of the encryption systems we currently use. However, if I don't have a solution handed to me for checking then it turns out that it is a difficult problem. Can a particular cube be solved in exactly n moves? This is an NP problem because, if you give me an n-move sequence that solves the cube, I can check and hence prove that it can be solved in n moves in polynomial time. We first have to convert the Rubik cube into a decision problem. This is a result that was obtained by Erik Demaine, Sarah Eisenstat, and Mikhail Rudoy - the team that has produced the latest result. ![]() What we do know is that god's number increases like n 2/log n. Finding the value for larger cubes in the same way would take far too long. It took several years of computing time to find the value for the 3x3x3 cube by what amounts to brute force calculation. However, it is worth pointing out that we don't know god's number for any larger cube. There are only around 300,000,000 positions that require 20 moves to reach a solution. This seems all the more remarkable when you are told that there are 43,252,003,274,489,856,000 potential positions The majority of solutions take between 15 and 19 moves to solve. I suppose that 20 moves isn't that many for any starting point for a 3x3x3 cube and this suggests that the task isn't that hard after all. For example, we know that any 3x3x3 cube can be solved in a maximum of 20 moves and this is known as "god's number" because it is assumed that to know it you have to be a god. Rubik's cube is a combinatorial puzzle that has generated a lot of interesting math. It has now been proved that working out if a random cube is solvable in exactly n moves is NP complete. ![]() If you find solving Rubik's cube difficult you will be pleased to learn that it really is.
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