________________
DECEMBER, 1924)
THE KNIGHT'S TOUR AT CHESS
263
Also in Plates V and VI it will be seen that the second half of the moves 33 to are in exactly the opposite squares of the board diagonally to those in the first half, 1 to :) This fact becomes quite clear if the board be divided, as in Plate VII, into quarters for convenience of noting the places of the respective figures.
Table A below, taken with Plates V, VI and VII, shows how the two halves of the board ctly correspond diagonally with the Symmetrical Knight's Tour. Thus :
TABLE A. DIAGONAL OPPOSITES IN THE SYMMETRICAL KNIGHT'S TOUR. First Second First Second First Second First Second with with with
with Half Hali Half
Half Half Half Half Half
49
57
32
48
64 I give also Table B showing how the two halves of the board correspond diagonally in the case of the Correct Knight's Tour (Plate IV, Fig. A). It will be seen that there is consi. derable, but by no means completely, exact correspondence. That is to say, the 1st and 3rd quarters of the board correspond exactly, but there is a certain confusion in the 2nd and 4th quarters. Thus :
TABLE B. DIAGONAL OPPOSITES IN THE CORRBOT KNIGHT'S TOUR. First Second First Second First Second First
Second
with Half Half
Half
Half Half
I
woond
.. with
with
with avond
HALE
