Starting with an ordinary 8x8 chessboard, perform a series of shifts to move all the black and white squares into contiguous colors. A "shift" is a push of one row (A-H) from left to right, or one column (1-8) from top to bottom. When a row is shifted right, the square shifted out is moved to the far left to keep the 8x8 square. Similarly, for a column shift, the square shifted out is moved to the top.
What is the fewest number of shifts needed to make all the black squares be contiguous and all the white squares be contiguous? What is the fewest number of shifts needed to just make a contiguous group of black squares?
01234567 A 01010101 B 10101010 C 01010101 D 10101010 E 01010101 F 10101010 G 01010101 H 10101010The following pattern of moves yield both contiguous areas of 1 and 0:
2C4E6AG 01234567 A 11111110 B 10001010 C 11101010 D 10000010 E 11111010 F 10000000 G 11111110 H 10000000Another nice permutation of the above moves is:
246ACEG 01234567 A 11111110 B 10000000 C 11111110 D 10000000 E 11111110 F 10000000 G 11111110 H 10000000No set of 6 moves creates a contiguous region. Note: I did my moves up and left instead of down and right, but the answer should be the same.