ShishNashKi

Whats up? A mathematical puzzle, a little group permutations, two problems for narrow-minded ones and a facet of a joke. Beg your pardon , if this puzzle is invented before me and I am a miserable ignorant, imagining that he invented something new. In the case of licensed purity, I call it ShishNashKi from now and forever and ever. Amen.

In the footsteps of publication

The human genius in the person of Mrrl solved the task of God in his mind in 20 moves.
Video solutions

Formulation of the problem

A 4x4 cell board with randomly mixed numbers from 1 to 16 is given.
')

Random alignment

It is necessary to rearrange all cells in ascending order, starting from the upper left corner of the board. A permutation is the rotation of any 4 neighboring cells on pi / 2 , pi and minus pi / 2 .

An example of a permutation in a mathematical notation (turning on the -fi lower right corner):

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 01 02 03 04 05 06 07 08 09 10 15 11 13 14 16 12 

The puzzle is a bit like a Rubik's Cube, but there are nuances. There are no symmetry groups (I will not go into the details of the mathematical theory of the Kyrgyz Republic). And any of the 16! layouts are solved. This theorem is fairly easy to prove by solving problem number 1.

Task number 1

Find a combination of permutations that interchange two blue cells.


Alignment of task number 1

Task number 2

Find the number of God for this puzzle. The number of God is the minimum number of moves with the help of which any deal is solved. For example, for the Rubik's Cube, in 2008 this number was 23, and now it’s already 20. The problem was solved by going through all the layouts. My task is simpler, but also not sugar: 16 - not horseradish, say thank you, that the author did not choose the 5x5 board.

I decided that the worst possible plan was a complete inversion of the board. In this case, each cell must be pulled through the entire field.


Initial worst deal

Having suffered a little and started from the number of God = 39, I reached 30.


Fake table of records in achieving the number of God

I think there are a couple of people on Habré who will find the number of God equal to 25. Well, well, well, Mrrl , not two, but three people.

Who wants to play on the iPhone, the game is ready for free testing. From you - apple id.