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Amusements in Mathematics

Unclassified Problems
"A snapper up of unconsidered trifles."
Winter's Tale, iv. 2.
Anderson, Biggs, and Carpenter were staying together at a place by the seaside. One day
they went out in a boat and were a mile at sea when a rifle was fired on shore in their
direction. Why or by whom the shot was fired fortunately does not concern us, as no
information on these points is obtainable, but from the facts I picked up we can get
material for a curious little puzzle for the novice.
It seems that Anderson only heard the report of the gun, Biggs only saw the smoke, and
Carpenter merely saw the bullet strike the water near them. Now, the question arises:
Which of them first knew of the discharge of the rifle?
There is a certain village in Japan, situated in a very low valley, and yet the sun is nearer
to the inhabitants every noon, by 3,000 miles and upwards, than when he either rises or
sets to these people. In what part of the country is the village situated?
If the end of the world should come on the first day of a new century, can you say what
are the chances that it will happen on a Sunday?
The illustration represents one of the most ancient of all mechanical puzzles. Its origin is
unknown. Cardan, the mathematician, wrote about it in 1550, and Wallis in 1693; while it
is said still to be found in obscure English villages (sometimes deposited in strange
places, such as a church belfry), made of iron, and appropriately called "tiring-irons," and
to be used by the Norwegians to-day as a lock for boxes and bags. In the toyshops it is
sometimes called the "Chinese rings," though there seems to be no authority for the
description, and it more frequently goes by the unsatisfactory name of "the puzzling
rings." The French call it "Baguenaudier."
The puzzle will be seen to consist of a simple loop of wire fixed in a handle to be held in
the left hand, and a certain number of rings secured by wires which pass through holes in
the bar and are kept there by their blunted ends. The wires work freely in the bar, but
cannot come apart from it, nor can the wires be removed from the rings. The general
puzzle is to detach the loop completely from all the rings, and then to put them all on