Amusements in Mathematics HTML version

"Dost thou not see that the sixty-four lights add up an even number vertically and
horizontally, but that all the diagonal lines, except fourteen are of a number that is odd?
Why is this?"
"Of a truth, my Lord Abbot, it is of the very nature of things, and cannot be changed."
"Nay, but it shall be changed. I command thee that certain of the lights be closed this day,
so that every line shall have an even number of lights. See thou that this be done without
delay, lest the cellars be locked up for a month and other grievous troubles befall thee."
Father John was at his wits' end, but after consultation with one who was learned in
strange mysteries, a way was found to satisfy the whim of the Lord Abbot. Which lights
were blocked up, so that those which remained added up an even number in every line
horizontally, vertically, and diagonally, while the least possible obstruction of light was
Into how large a number of different pieces may the chessboard be cut (by cuts along the
lines only), no two pieces being exactly alike? Remember that the arrangement of black
and white constitutes a difference. Thus, a single black square will be different from a
single white square, a row of three containing two white squares will differ from a row of
three containing two black, and so on. If two pieces cannot be placed on the table so as to
be exactly alike, they count as different. And as the back of the board is plain, the pieces
cannot be turned over.
I once set myself the amusing task of so dissecting an ordinary chessboard into letters of
the alphabet that they would form a complete sentence. It will be seen from the
illustration that the pieces assembled give the sentence, "CUT THY LIFE," with the stops
between. The ideal sentence would, of course, have only one full stop, but that I did not
succeed in obtaining.
The sentence is an appeal to the transgressor to cut himself adrift from the evil life he is
living. Can you fit these pieces together to form a perfect chessboard?
"They also serve who only stand and wait."