Place ten pennies on a large sheet of paper or cardboard, as shown in
the diagram, five on each edge. Now remove four of the coins, without
disturbing the others, and replace them on the paper so that the ten
shall form five straight lines with four coins in every line. This in
itself is not difficult, but you should try to discover in how many
different ways the puzzle may be solved, assuming that in every case the
two rows at starting are exactly the same.
[Illustration]
211.--THE TWELVE MINCE-PIES.
It will be seen in our illustration how twelve mince-pies may be placed
on the table so as to form six straight rows with four pies in every
row. The puzzle is to remove only four of them to new positions so that
there shall be _seven_ straight rows with four in every row. Which four
would you remove, and where would you replace them?
[Illustration]
212.--THE BURMESE PLANTATION.
[Illustration]
A short time ago I received an interesting communication from the
British chaplain at Meiktila, Upper Burma, in which my correspondent
informed me that he had found some amusement on board ship on his way
out in trying to solve this little poser.
If he has a plantation of forty-nine trees, planted in the form of a
square as shown in the accompanying illustration, he wishes to know how
he may cut down twenty-seven of the trees so that the twenty-two left
standing shall form as many rows as possible with four trees in every
row.
Of course there may not be more than four trees in any row.
213.--TURKS AND RUSSIANS.
This puzzle is on the lines of the Afridi problem published by me in
_Tit-Bits_ some years ago.
On an open level tract of country a party of Russian infantry, no two of
whom were stationed at the same spot, were suddenly surprised by
thirty-two Turks, who opened fire on the Russians from all directions.
Each of the Turks simultaneously fired a bullet, and each bullet passed
immediately over the heads of three Russian soldiers. As each of these
bullets when fired killed a different man, the puzzle is to discover
what is the smallest possible number of soldiers of which the Russian
party could have consisted and what were the casualties on each side.
MOVING COUNTER PROBLEMS.
"I cannot do't without counters."
_Winter's Tale_, iv. 3.
Puzzles of this class, except so far as they occur in connection with
actual games, such as chess, seem to be a comparatively modern
introduction. Mathematicians in recent times, notably Vandermonde and
Reiss, have devoted some attention to them, but they do not appear to
have been considered by the old writers. So far as games with counters
are concerned, perhaps the most ancient and widely known in old times is
"Nine Men's Morris" (known also, as I shall show, under a great many
other names), unless the simpler game, distinctly mentioned in the works
of Ovid (No. 110, "Ovid's Game," in _The Canterbury Puzzles_), from
which "Noughts and Crosses" seems to be derived, is still more ancient.
Public-domain text, read in full here on John Shaqi.
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