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Amusements in Mathematics

of doing it. How many different ways are there altogether? A piece which when turned
over resembles another piece is not considered to be of a different shape.
291.—THE GRAND LAMA'S PROBLEM.
Once upon a time there was a Grand Lama who had a chessboard made of pure gold,
magnificently engraved, and, of course, of great value. Every year a tournament was held
at Lhassa among the priests, and whenever any one beat the Grand Lama it was
considered a great honour, and his name was inscribed on the back of the board, and a
costly jewel set in the particular square on which the checkmate had been given. After
this sovereign pontiff had been defeated on four occasions he died—possibly of chagrin.
Now the new Grand Lama was an inferior chess-player, and preferred other forms of
innocent amusement, such as cutting off people's heads. So he discouraged chess as a
degrading game, that did not improve either the mind or the morals, and abolished the
tournament summarily. Then he sent for the four priests who had had the effrontery to
play better than a Grand Lama, and addressed them as follows: "Miserable and
heathenish men, calling yourselves priests! Know ye not that to lay claim to a capacity to
do anything better than my predecessor is a capital offence? Take that chessboard and,
before day dawns upon the torture chamber, cut it into four equal parts of the same shape,
each containing sixteen perfect squares, with one of the gems in each part! If in this you
fail, then shall other sports be devised for your special delectation. Go!" The four priests
succeeded in their apparently hopeless task. Can you show how the board may be divided
into four equal parts, each of exactly the same shape, by cuts along the lines dividing the
squares, each part to contain one of the gems?
292.—THE ABBOT'S WINDOW.
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.
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