The Seventh Guest Help from Neil Shipman One of the puzzles which seems to give people the most difficulty is interchanging the positions of the bishops on the chessboard. ----------------------------------------- | | | | | | 4 | | | | | | | | | | | | ----------------------------------------- | | | | | | 3 | | | | | | | | | | | | ----------------------------------------- | | | | | | 2 | | | | | | | | | | | | ----------------------------------------- | | | | | | 1 | | | | | | | | | | | | ----------------------------------------- a b c d e Firstly, it's obvious that there are two distinct sets of bishops to be swapped: those on the white squares and those on the black. There is of course no interaction between these two sets. We'll tackle the ones on the white squares first. Make the following moves: e2 - d3 : a4 - d1 : a2 - b3 : d3 - b1 : b3 - a4 : e4 - d3 : b1 - a2 : d3 - c4 : d1 - c2 : c2 - e4 : c4 - e2 : a2 - c4 : a4 - c2 : c2 - b1 : e2 - d1 : d1 - a4 : c4 - b3 : b1 - d3 : b3 - a2 : d3 - e2 Now the moves of the black square bishops are simply done if you just visualise the board turned through 180 degrees, thus: a3 - b2 : e1 - b4 : e3 - d2 : b2 - d4 : d2 - e1 : a1 - b2 : d4 - e3 : b2 - c1 : b4 - c3 : c3 - a1 : c1 - a3 : e3 - c1 : e1 - c3 : c3 - d4 : a3 - b4 : b4 - e1 : c1 - d2 : d4 - b2 : d2 - e3 : b2 - a3 - o -