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Rubik's Cube Challenge Mystery Cache

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Hidden : 5/7/2013
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


This mystery cache is dedicated to the most popular and famous puzzle in the world - Rubik's Cube. Bad part - the given coordinates won't lead you to the cache. But the good part is that you don't necessarily should be able to solve the cube fully to get the real coordinates of the cache. The task is just logical.



About the puzzle:
Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via German businessman Tibor Laczi and Seven Towns founder Tom Kremer, and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide making it the world's top-selling puzzle game.

In a classic 3x3x3 Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours (traditionally white, red, blue, orange, green, and yellow, where white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement). An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to consisting of one colour. Similar puzzles have now been produced with various numbers of sides, dimensions ( 2×2×2, 4x4x4, 5×5×5, 6×6×6, 7×7×7 and 11×11×11), and stickers, not all of them by Rubik. In 2011, Guinness World Records awarded the "largest order Rubiks magic cube" to a 17x17x17 cube, made by Oskar van Deventer.

A standard Rubik's Cube measures 5.7 cm on each side, consists of twenty-six unique miniature cubes and has the centre piece, a "3-D cross", which connects all the parts. It has eight corners and twelve edges. What is unbelievable, is that there are 8!x3^7x(12!/2)x2^11 = 43,252,003,274,489,856,000 possible arrangements of the pieces that make up the Cube and could be reached by moving the sides of it. To put this into perspective, if one had as many standard sized Rubik's Cubes as there are permutations, one could cover the Earth's surface 275 times.

Many general solutions for the Rubik's Cube have been discovered independently. The most popular method was developed by David Singmaster and published in the book Notes on Rubik's "Magic Cube" in 1981. This solution involves solving the Cube layer by layer, in which one layer (designated the top) is solved first, followed by the middle layer, and then the final and bottom layer. After sufficient practice, solving the Cube layer by layer can be done in under one minute. Other general solutions include "corners first" methods or combinations of several other methods. In 1982, David Singmaster and Alexander Frey hypothesised that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration can be solved in 26 moves or fewer. In 2008, Tomas Rokicki lowered that number to 22 moves, and in July 2010, a team of researchers including Rokicki, working with Google, proved the so-called "God's number" to be 20.

Speedcubing

A solution commonly used by speed cubers was developed by Jessica Fridrich. It requires learning roughly 120 algorithms but allows the Cube to be solved in only 55 moves on average. The first world championship organised by the Guinness Book of World Records was held in Munich on March 13, 1981. All Cubes were moved 40 times and lubricated with petroleum jelly. The official winner, with a record of 38 seconds, was Jury Froeschl, born in Munich. The first international world championship was held in Budapest on June 5, 1982, and was won by Minh Thai, a Vietnamese student from Los Angeles, with a time of 22.95 seconds. Since 2003, the winner of a competition is determined by taking the average time of the middle three of five attempts. However, the single best time of all tries is also recorded. The current world record for single time on a 3×3×3 Rubik's Cube was set by Mats Valk of the Netherlands in March 2013 with a time of 5.55 seconds at the Zonhoven Open in Belgium (video). The world record for average time per solve was set by Feliks Zemdegs at the Australian Nationals 2012, with a 7.53 second average solve time. The fastest non-human time for a physical 3×3×3 Rubik's Cube is 5.270 seconds, set by CubeStormer II, a robot built using Lego Mindstorms and a Samsung Galaxy S2.

In addition to official competitions, informal alternative competitions have been held which invite participants to solve the Cube in unusual situations. Some such situations include:
-Blindfolded solving;
-Solving the Cube with one person blindfolded and the other person saying what moves to make, known as "Team Blindfold";
-Multiple blindfolded solving, or "multi-blind", in which the contestant solves any number of cubes blindfolded in a row;
-Solving the Cube underwater in a single breath;
-Solving the Cube using a single hand;
-Solving the Cube with one's feet;
-Solving the Cube in the fewest possible moves;

More information could be found here.

Few easiest and the most obvious methods of solving the Cube for beginners are here and here.


Task:
First of all, notation of Rubik's Cube: The cube has six faces:
  F = front face
  B = back face
  R = right face
  L = left face
  U = up face
  D = down face.
In our task front face will be red, back face - orange, and so on, as it is shown in this picture:

   

In addition to a letter, each move may be accompanied by an apostrophe or the number two:
A letter by itself means turn that face 90 degrees clockwise (eg. F).
A letter followed by an apostrophe means turn that face 90 degrees anti-clockwise (eg. F').
A letter followed by the number 2 means turn that face 180 degrees (direction is irrelevant), (eg. F2).
So R U' L2 is shorthand for "turn the right face 90 degrees clockwise, then turn the up face 90 degrees anti-clockwise, then turn the left face 180 degrees". When thinking whether to turn clockwise/anti-clockwise, imagine that you are looking directly at the particular face you are turning.

So, your task will be to solve the Cube three times (when it is scrambled with 5 moves, 6 moves and 7 moves). In other words you will need only to puzzle out which moves were taken to scramble the Cube, and made them conversely to solve it. While solving you should write down the moves that you made (5 moves in first case, 6 in second and 7 in third). Then use these equalities to convert moves (letters) to numbers:

  F = 1   F' = 7   F2 = 13
  B = 2   B' = 8   B2 = 14
  R = 3   R' = 9   R2 = 15
  L = 4   L' = 10   L2 = 16
  U = 5   U' = 11   U2 = 17
  D = 6   D' = 12   D2 = 18

After that you will have three long numbers X, Y and Z. For example: if in first task you solved the Cube by taking moves RUD2B'L, you will get number X=351884, because R=3, U=5, D2=18, B'=8 and L=4.

And when you have numbers X,Y,Z, just enter them into the formula of final coordinates of the cache:

(X+Y+Z)*26576 + Z - 6*X - 26337885 = FINAL COORDINATES

I hope everything is clear. Are you ready? Then here the tasks are:

   TASK 1 (Solve the Cube with 5 moves and get number X):

   

   TASK 2 (Solve the Cube with 6 moves and get number Y):

   

   TASK 3 (Solve the Cube with 7 moves and get number Z):

   

You can check your solution here:



Little bit of logic and Rubik's Cube Challenge will be done! Solve and find it! Good Luck!

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Additional Hints (Decrypt)

Qivthonf Cb / Qhny Haqre

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)