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.

It was found on an old Roman tile discovered during the excavations at Silchester, and cut upon the steps of the Acropolis at Athens.  When visiting the Christiania Museum a few years ago I was shown the great Viking ship that was discovered at Gokstad in 1880.  On the oak planks forming the deck of the vessel were found boles and lines marking out the game, the holes being made to receive pegs.  While inspecting the ancient oak furniture in the Rijks Museum at Amsterdam I became interested in an old catechumen’s settle, and was surprised to find the game diagram cut in the centre of the seat—­quite conveniently for surreptitious play.  It has been discovered cut in the choir stalls of several of our English cathedrals.  In the early eighties it was found scratched upon a stone built into a wall (probably about the date 1200), during the restoration of Hargrave church in Northamptonshire.  This stone is now in the Northampton Museum.  A similar stone has since been found at Sempringham, Lincolnshire.  It is to be seen on an ancient tombstone in the Isle of Man, and painted on old Dutch tiles.  And in 1901 a stone was dug out of a gravel pit near Oswestry bearing an undoubted diagram of the game.

The game has been played with different rules at different periods and places.  I give a copy of the board.  Sometimes the diagonal lines are omitted, but this evidently was not intended to affect the play:  it simply meant that the angles alone were thought sufficient to indicate the points.  This is how Strutt, in Sports and Pastimes, describes the game, and it agrees with the way I played it as a boy:—­“Two persons, having each of them nine pieces, or men, lay them down alternately, one by one, upon the spots; and the business of either party is to prevent his antagonist from placing three of his pieces so as to form a row of three, without the intervention of an opponent piece.  If a row be formed, he that made it is at liberty to take up one of his competitor’s pieces from any part he thinks most to his advantage; excepting he has made a row, which must not be touched if he have another piece upon the board that is not a component part of that row.  When all the pieces are laid down, they are played backwards and forwards, in any direction that the lines run, but only can move from one spot to another (next to it) at one time.  He that takes off all his antagonist’s pieces is the conqueror.”

[Illustration]

214.—­THE SIX FROGS.

[Illustration]

The six educated frogs in the illustration are trained to reverse their order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank square in its present position.  They can jump to the next square (if vacant) or leap over one frog to the next square beyond (if vacant), just as we move in the game of draughts, and can go backwards or forwards at pleasure.  Can you show how they perform their feat in the fewest possible moves?  It is quite easy, so when you have done it add a seventh frog to the right and try again.  Then add more frogs until you are able to give the shortest solution for any number.  For it can always be done, with that single vacant square, no matter how many frogs there are.

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Amusements in Mathematics from Project Gutenberg. Public domain.