K. 176. Alex is playing the game called Bloxorz. It involves rolling a rectangular block on a board with a lattice of unit squares. The base of the block is a unit square and its height is two units. The block always covers one or two fields of the board. The first Figure shows the allowed moves of the block.
In each move, the block is turned around an edge so that it lands on a face adjacent to the bottom. During the game, it is not allowed for the block to leave the board, that is, it cannot even partly overhang the edge. The purpose of the game is to move the block from the starting position to a standing position on the field marked X (that is, it should only touch that field of the board). (See http://miniclip.com/games/bloxorz/en for the internet version of the game.)
The second Figure shows the board. Initially, the block is standing on the black field. Move the block to the field marked X, in a standing position. Draw the successive intermediate positions of the block (indicating the order with numbers), through which it gets to the field marked X. Keep marking the positions on the same diagram until the next position overlaps with some previous position. Then draw a new diagram and continue to show further positions. Find a solution that consists of less than 30 steps.
This problem is for grade 9 students only.