1. What is the minimal number of 90-degree turns for a bishop to walk through all the black squares of a standard 8*8 chessboard, starting at h8 and terminating at a1?

2. What if in question 1 the word "black" is erased and the word "bishop" is replaced by "rook"?

I've only ever seen the first as asking to traverse the board in the fewest straight lines but the right angles are where one would terminate each line.
[a1]
 e5, b8, a7, g1
 h2, f4,  c1, a3
 f8,  h6, g5, h4
 e1, a5, d8,  f6
                 [h8]

For the second one is tempted to rush in and go and down the files or cross the ranks but that brings you back to the same rank or file from which you began.

Some backtracking is necessary. 
Beginning with file a I traversed up and down until arriving at the top of file g. I turned to the left and came down file f once again and turned to file h and went to the top of the board to complete my journey.

Although the latter journey need not be as mine I see no fewer turns thus I declare 16 right turns in both cases.

Posted by brianjn on 2011-01-25 21:10:18