THE ABBOT'S WINDOW.
(
Chessboard Problems)
Once upon a time the Lord Abbot of St. Edmondsbury, in consequence of
"devotions too strong for his head," fell sick and was unable to leave
his bed. As he lay awake, tossing his head restlessly from side to side,
the attentive monks noticed that something was disturbing his mind; but
nobody dared ask what it might be, for the abbot was of a stern
disposition, and never would brook inquisitiveness. Suddenly he called
for Father John, and that venerable monk was soon at the bedside.
"Father John," said the Abbot, "dost thou know that I came into this
wicked world on a Christmas Even?"
The monk nodded assent.
"And have I not often told thee that, having been born on Christmas
Even, I have no love for the things that are odd? Look there!"
The Abbot pointed to the large dormitory window, of which I give a
sketch. The monk looked, and was perplexed.
"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
caused?
Answer:
THE man who was "learned in strange mysteries" pointed out to Father
John that the orders of the Lord Abbot of St. Edmondsbury might be
easily carried out by blocking up twelve of the lights in the window as
shown by the dark squares in the following sketch:--
[Illustration:
+===+===+===+===+===+===+===+===+
| : : : : : : : |
I...+===+...+...+...+...+===+...I
| IIIII : : : IIIII |
I...+===+===+...+...+===+===+...I
| : IIIII : IIIII : |
I...+...+===+===+===+===+...+...I
| : : IIIIIIIII : : |
I...+...+...+===+===+...+...+...I
| : : IIIIIIIII : : |
I...+...+===+===+===+===+...+...I
| : IIIII : IIIII : |
I...+===+===+...+...+===+===+...I
| IIIII : : : IIIII |
I...+===+...+...+...+...+===+...I
| : : : : : : : |
+===+===+===+===+===+===+===+===+
]
Father John held that the four corners should also be darkened, but the
sage explained that it was desired to obstruct no more light than was
absolutely necessary, and he said, anticipating Lord Dundreary, "A
single pane can no more be in a _line_ with itself than one bird can go
into a corner and flock in solitude. The Abbot's condition was that no
diagonal _lines_ should contain an odd number of lights."
Now, when the holy man saw what had been done he was well pleased, and
said, "Truly, Father John, thou art a man of deep wisdom, in that thou
hast done that which seemed impossible, and yet withal adorned our
window with a device of the cross of St. Andrew, whose name I received
from my godfathers and godmothers." Thereafter he slept well and arose
refreshed. The window might be seen intact to-day in the monastery of
St. Edmondsbury, if it existed, which, alas! the window does not.
Informational
