Amusements in Mathematics eBook

Henry Dudeney
This eBook from the Gutenberg Project consists of approximately 597 pages of information about Amusements in Mathematics.

Amusements in Mathematics eBook

Henry Dudeney
This eBook from the Gutenberg Project consists of approximately 597 pages of information about Amusements in Mathematics.

“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?

293.—­THE CHINESE CHESSBOARD.

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.

294.—­THE CHESSBOARD SENTENCE.

[Illustration]

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?

STATICAL CHESS PUZZLES.

    “They also serve who only stand and wait.” 
                                MILTON.

295.—­THE EIGHT ROOKS.

[Illustration: 

+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| R | R | R | R | R | R | R | R |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   |   |   |   |   |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+

FIG. 1.]

[Illustration: 

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Amusements in Mathematics from Project Gutenberg. Public domain.