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MISCELLANEOUS PUZZLES
ten, or stop your making seventeen, twenty-four, and the winning
thirty-one. You have only to secure these numbers to win."
But this is just that little knowledge which is such a dangerous
thing, and it places you in the hands of the sharper.
You play 3, and the sharper plays 4 and counts "seven" ; you
play 3 and count "ten"; the sharper turns down 3 and scores
" thirteen" ; you play 4 and count" seventeen " ; the sharper plays a
4 and counts " twenty-one "; you play 3 and make your'' twenty-four."
Now the sharper plays the last 4 and scores " twenty-eight."
You look in vain for another 3 with which to win, for they are
all turned down ! So you are compelled either to let him make the
" thirty-one " or to go yourself beyond, and so lose the game.
You thus see that your method of certainly winning breaks down
utterly, by what may be called the " method of exhaustion." I will
give the key to the game, showing how you may always win ; but I
will not here say whether you must play first or second : you may
like to find it out for yourself.
80.
The Chinese Railways.
Our illustration shows the plan of a Chinese city protected by
pentagonal fortifications. Five European Powers were scheming
and clamouring for a concession to run a railway to the place ; and
at last one of the Emperor's
more brilliant advisers said,
" Let every one of them
have a concession ! " So
the Celestial Government
officials were kept busy ar-
ranging the details. The
letters in the diagram show
the different nationalities,
and indicate not only just
where each line must enter the city, but also where the station
belonging to that line must be located. As it was agreed that
the line of one company must never cross the line of another,
the representatives of the various countries concerned were
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