We are not a great advocate for arithmetical puzzles as a pastime for
festive occasions, that is to say not as a general rule; but there are
certain tricks of figures which are quite amusing, and some few problems
which from their very simplicity become almost ludicrous. We have seen
many a tolerably wise head puzzled over the question:
"If a barrel of flour cost thirty-nine dollars thirteen and three
quarter cents, what will a penny loaf come to?"
And consume considerable time and paper without discovering the obvious
fact, that a penny loaf will of course come to a penny and nothing else.
We remember, too, an amiable Divine, who tortured his dear old head for
three-quarters of an hour to solve the question:
"If a shovel, poker, and tongs, cost thirteen dollars forty-three and a
quarter cents, what will a ton of coals come to?"
And when informed that they would come to ashes, he seemed to feel quite
hurt; and indeed, to labor for some time under a sense of having been
trifled with. When told that it was merely a joke, a little fun, he
replied that he was a great admirer of Don Quixote, could appreciate Gil
Bias, and relished exceedingly the wit of Swift and Sterne; but failed
to perceive the particular humor of our joke about the ton of coals.
With all due respect for the estimable prelate, we must venture to
differ from him, fortified as we are in our opinion by a young lady,
who, if not a divine herself, has a pair of eyes that are, in whose
company we have solved some of the most intricate arithmetical
jocularities and trivialities, till we were up to the eyes in ink and
love. One we well remember, partly because it gave us so much trouble,
and partly because there was a wild picturesqueness about the subject
which appeals to our imagination. It ran thus:
A man has a wolf, a goat, and a cabbage, to carry over a river, but he
can only convey them one at a time, his boat being very small. How is he
to manage this, so that the wolf may not be left alone with the goat,
nor the goat with the cabbage? It is obvious if the wolf be left with
the goat, he will eat it up; whilst if the goat be left with the
cabbage, short work will be made of that classic vegetable.
Oh, how often we crossed and recrossed that river; how often we took the
goat out, and put the wolf in; and how frequently we took out the wolf,
and put in the goat. How we trembled for the poor man, fearing there
could be no alternative for him but to sacrifice either the goat or the
cabbage, or else kill the wolf. How varied and wild were our expedients,
such as throwing the wolf across, sending the cabbage round by express,
digging a tunnel under the bed of the river, forcing the proprietor to
eat the cabbage himself, towing the goat behind the boat, and other
devices too numerous to mention, all of which we were assured, by those
holding the key to the mystery, were altogether inadmissible; and then
when, with humbled pride, we reluctantly _gave it up_, how mad we were
at the simplicity of the solution, which was this:
He first takes over the goat, and then returns for the wolf; he then
takes back the goat, which he leaves, and takes over the cabbage, he
then returns and takes over the goat All as simple as A, B, C, when _you
know how to do it_; that knowing how to do it is the great difficulty in
ninety-nine out of every hundred things in this world.
Puzzles which involve long and laborious calculation are not in our
line; they are too suggestive of the school and the country room.
Something like the following is good for skirmishing:
PROBLEM.
Put down four nines, so that they will make one hundred.
After a short struggle you surrender at discretion, and in an instant
get the
SOLUTION.
99-9/9
There is no delay, no tedious figuring up; you get your answer and are
ready for something fresh. Some such abstruse calculation as the
following, for instance:
PROBLEM.
If a herring and a half cost three cents, how many will you get for a
dollar?
To ladies, who as a general rule have not the organ of calculation very
largely developed, this will usually prove a poser. As the problem is to
be solved by patience and study, we will leave them to do it, _or give
it up_, and proceed to the next
PROBLEM.
A gentleman sent his servant with a present of nine ducks in a box, upon
which was the following direction:--
"To Alderman Gobble with IX. ducks."
The servant, who had more ingenuity than honesty, purloined three of the
ducks, and contrived it so that the number contained in the box
corresponded with that upon the direction. As he neither erased any word
or letter, nor substituted a new direction, how did he so alter it as to
correspond with the contents of the box?
The dishonest but ingenious servant simply placed the letter S before
the two Roman numerals, IX. The direction then read thus:
"To Alderman Gobble, with SIX ducks."
It will be seen that this problem is very easy of solution to every one,
save Artemus Ward, who would spell it _Sicks dux in a bocks_.
Here is one, however, which would suit the taste, if not the ability, of
the great showman to a nicety:
PROBLEM.
To distribute among three persons twenty-one casks of wine, seven of
them full, seven of them empty, and seven of them half full; so that
each of them shall have the same quantity of wine, and the same number
of casks.
This problem admits of two solutions, which may be clearly comprehended
by means of the two following tables:
FIRST SOLUTION.
_Persons._ _Full casks._ _Empty._ _Half full._
1 2 2 3
2 2 2 3
3 3 3 1
SECOND SOLUTION.
_Persons._ _Full casks._ _Empty._ _Half full._
1 3 3 1
2 3 3 1
3 1 1 5
One more problem, and we shall have had enough mathematics for one
chapter.
[Illustration]
A figure similar to the preceding can be formed without removing the
pencil from the paper, without crossing any line or retracing any part.
Now set to work and do it.
If you do not succeed, you may refer to the annexed diagram and
solution.
[Illustration]
Draw a line from 1 to 2, 2 to 3, 3 to 4, 4 to 5, 5 to 6, 6 to 1, 1 to 7,
7 to 8, 8 to 9, 9 to 3, 3 to 10, and 10 to 1.