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.

99⁹/₉

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:—

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:

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:

One more problem, and we shall have had enough mathematics for one chapter.