Part 6

Suppose it were possible for a man in Cincinnati to start on Sunday noon, when the sun is in the meridian, and travel westward with the sun so that it might be in his meridian all the time. Now it was Sunday noon when he started, it has been noon with him all the way round, and is Monday noon when he returns. The question is, at what point did it change from Sunday noon to Monday noon?

Take any number, subtract the sum of the digits, strike out any digit from the remainder, tell me the sum of the remaining digits, and I will tell you the digit struck out.

METHOD.—Subtract the “sum of the remaining digits” from the smallest multiple of nine greater than “the sum.” The remainder will be the digit struck out.

In the bottom of a well, 45 feet deep, there was a frog which commenced traveling toward the top. In his journey he ascended 3 feet every day, but fell back 2 feet every night. In how many days did he get out?

METHOD.—He gains 1 foot a day, and in 42 days he is 3 feet from the top; and on the 43d day he reaches the top.

Think of any three numbers less than 10. Multiply the first by 2 and add 5 to the product. Multiply this sum by 5 and add the second number to the product. Multiply the last result by 10 and add the third number to the product; then subtract 250. Name the remainder and I will name the numbers thought of and in the order in which they were thought of.

METHOD.—The three digits composing this remainder will be the numbers thought of: and the order in which they were thought of will be the order of hundreds, tens, and units.

If a man had a triangular lot of land, the largest side being 136 rods, and each of the other sides 68 rods; what would be the value of the grass on it at the rate of $10 an acre?

REMARK.—The “catch” in this is that the sides given will form no triangle.

Says A to B: “Give me four weights and I can weigh any number of pounds not exceeding 40.” Required the weights and the method of weighing.

ANSWER.—The weights are 1, 3, 9, and 27 pounds. In weighing we must put one or more in both scales, or some in one scale and some in another: thus, 7 lbs. = 9 lbs. + 1 lb. - 3 lbs.

Three men traveling with their wives came to a river which they wished to cross. There was but one boat and but two could cross at one time; and since the husbands were jealous no woman could be with a man unless her own husband was present. In what manner did they get across the river?

METHOD.—Let the persons be denoted A, B, and C, and Mrs. A, Mrs. B, and Mrs. C. First Mr. A and Mrs. A go over; then A comes back and Mrs. B and Mrs. C go over; then Mrs. A comes back and Mr. B and Mr. C go over; then Mr. B and Mrs. B return and Mr. A and Mr. B go over; then Mrs. C returns and Mrs. A and Mrs. B go over; then Mr. C returns and takes his wife, Mrs. C, over.

A man having a fox, a goose, and some corn came to a river which it was necessary to cross. He could, however, take only one across at a time, and if he left the goose and corn while he took the fox over, the goose would eat the corn; but if he left the fox and goose, the fox would kill the goose. How shall he get them all safely over?

METHOD.—First he takes the goose over, then returns and takes the fox over, then brings the goose back and takes the corn over, and then returns and takes the goose over again.

How may the 9 digits be arranged in a rectangular form so that the sum of any row, whether horizontal, vertical, or diagonal, shall equal 15?

ANSWER.—As below.

+---+---+---+ | 4 | 9 | 2 | +---+---+---+ | 3 | 5 | 7 | +---+---+---+ | 8 | 1 | 6 | +---+---+---+

How may the first 16 digits be arranged so that the sum of the vertical, the horizontal, and the two oblique rows may equal 34?

ANSWER.—As below.

+----+----+----+----+ | 1 | 16 | 11 | 6 | +----+----+----+----+ | 13 | 4 | 7 | 10 | +----+----+----+----+ | 8 | 9 | 14 | 3 | +----+----+----+----+ | 12 | 5 | 2 | 15 | +----+----+----+----+

In what manner may the first 25 digits be arranged so that the sum of each row of five figures may equal 65?

ANSWER.—As below.

+----+----+----+----+----+ | 1 | 10 | 12 | 18 | 24 | +----+----+----+----+----+ | 9 | 11 | 20 | 22 | 3 | +----+----+----+----+----+ | 13 | 19 | 21 | 5 | 7 | +----+----+----+----+----+ | 17 | 23 | 4 | 6 | 15 | +----+----+----+----+----+ | 25 | 2 | 8 | 14 | 16 | +----+----+----+----+----+

An old Jew took a diamond cross to a jeweler to have the diamonds reset, and fearing the jeweler might be dishonest, he counted the diamonds and found that they numbered 7 in three different ways. Now the jeweler stole two diamonds, but arranged the remainder so that they counted 7 each way as before. How was it done?

Fig. 1. Fig. 2. 7 7 6 7 6 7 7 6 5 6 7 5 4 4 3 3 2 2 1 1

METHOD.—The form of the cross when left is represented by Fig. 1, and when returned by Fig. 2. It will be seen by the figures how the diamonds were counted by the old Jew, and how they were arranged by the jeweler, who “jewed” the Jew.

Take 10 pieces of money, lay them in a row, and require some one to put them together into heaps of two in each heap by passing each piece over two others.

METHOD.—Let the pieces be denoted by the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then place 7 on 10, 5 on 2, 3 on 8, 1 on 4, and 9 on 6.

A man goes to a store and purchases a pair of boots worth $5 and hands out a $50 bill to pay for them. The merchant, not being able to make the change, goes over the street to a broker and gets the bill changed and then returns and gives the man who bought the boots his change. After the purchaser of the boots had been gone a few hours the broker, finding the bill to be a counterfeit, comes and demands $50 of good money from the merchant. How much does the merchant lose?

REMARK.—At first glance some say $45 and the boots, some $50 and the boots, some $95 and the boots, and others $100 and the boots. Which is correct?

A vessel with a crew of 30 men, half of whom were black, became short of provisions and fearing that unless half the crew were thrown overboard all would perish, the captain proposed to the sailors to stand upon deck in a row and every ninth man be thrown overboard until half the crew were destroyed. It so happened that the whites were saved. Required, the order of arrangement.

ANSWER.—W W W W B B B B B W W B W W W B W B B W W B B B W B B W W B. This can easily be proved by trial, using letters or figures to represent men.

Suppose a hare is 10 rods before a hound, and that the hound runs 10 rods while the hare runs 1 rod. Now, when the hound has run 10 rods the hare has run 1 rod; hence they are now 1 rod apart, and when the hound has run that one rod the hare has run 1/10 of a rod; hence they are now 1/10 of a rod apart, and when the hound has run the 1/10 of a rod they are 1/100 of a rod apart; and in the same way it may be shown the hare is always 1/10 of the previous distance ahead of the hound; hence the hound can never catch the hare. How is the contrary shown mathematically? How far will the hound run to catch the hare.

ANSWER.—The distance the hound runs will be represented by the series

1 1 1 10 + 1 + ——— + ——— + ————, 10 100 1000

to infinity. The sum of this series can be found by the algebraic formula

_a_ S = ———————, (1 - _r_)

in which _a_ = 10 and _r_ = 1/10. Substituting the value of _a_ and _r_ we have

10 10 ——————— ————— 100 S = 1 = 9 = ——— = 11-1/9. 1 - ——— ——— 9 10 10

This may be solved more simply as follows: The hound runs 10 times as fast as the fox, hence 10 times the distance the fox runs equals the distance the hound runs. Then 10 times the distance the fox runs, minus once the distance the fox runs, which is 9 times the distance the fox runs, is 10 rods; and once the distance the fox runs is 1/9 of 10 rods, or 10/9 rods; and 10 times the distance the fox runs, or the distance the hound runs, is 10 times 10/9 or 100/9, or 11-1/9 rods.

If through passenger trains, running to and from Philadelphia and San Francisco daily, start at the same hour from each place (difference of longitude not being considered) and take the same time—seven days—for the trip, how many through trains will the Pacific Express, that leaves the San Francisco depot at 9 P. M. Sunday, have met when it reaches the Philadelphia depot?

ANSWER.—As the Pacific Express starts from San Francisco, a train which left Philadelphia the previous Sunday reaches San Francisco, which is not to be counted as a meeting of trains. There are, however, six other trains on the way which it will meet. Also, a train starts from Philadelphia on the same Sunday as the train starts from San Francisco, another on Monday, another on Tuesday, etc., up to Saturday—that is, seven trains, all of which it meets, making, with the six trains previously started, thirteen trains in all which it meets. A train leaves Philadelphia on Sunday at the same time the Pacific Express reaches there, but this is not counted as a meeting.

A switch siding to a single-track railroad is just long enough to clear a train of eight cars and a locomotive. How can two trains of sixteen cars and a locomotive, each going in opposite directions, pass each other at this siding and each locomotive remain with, and have the same relative position to its own train after as before passing?

ANSWER.—Let one train and its locomotive be denoted by A, and the other train and locomotive by B, and let the track be denoted by _a b_ and the siding by _c d_, and suppose train A to be going in the direction of _a b_, and train B in the direction of _b a_. Then let locomotive B, with eight cars, run out toward _a_, past _c_, and back up on the siding with its eight cars; then let train A run out toward _b_, past _c_; then let B draw its eight cars on to the main track and run out toward _a_; then let train A back over toward _a_, past _c_, and locomotive A be detached from train A and run over toward _b_ and connect with the eight cars of train B and draw them over past _c_, and back them up on the siding, and then run off the siding and connect again with its own cars and run on toward _b_, past _c_; then let locomotive B back its eight cars and, turning on the siding, connect the two halves of its train and move off past _a_, the train A moving on at the same time past _b_.

A and B went to market with 30 pigs each. A sold his pigs at 2 for $1, and B sold his pigs at the rate of 3 for $1, and they, together, received $25. The next day A went to market alone with 60 pigs, and, wishing to sell at the same rate, sold them 5 for $2, and received only $24. Why should he not receive as much as when B owned half of the pigs?

ANSWER.—The rate of 2 pigs for $1 is 1 pig for $½, and the rate of 3 pigs for $1 is 1 pig for $⅓; the average rate is 2 pigs for $½ + $⅓, or $⅚, or 1 pig for $5/12. The rate of 5 pigs for $2 is 1 pig for $⅖. So it is seen that the reason A did not receive as much is that he sold his pigs at a less rate than when they both went to market.

Two hunters killed a deer and sold it by the pound in the woods. They had no proper means of weighing it, but knew their own weights—one 130 pounds and the other 190 pounds. They placed a rail across a fence so that it balanced with one of them on each end. They then exchanged places, the lighter man taking the deer in his lap, and the rail again balanced; what was the weight of the deer?

ANSWER.—Let the weight of the deer be denoted by D; then, by the principles of the lever, we have the proportion:

130 : 190 = 190 : 130 + D: Or, 130 (130 + D) = 190 × 190; Whence, 16900 + 130 D = 36100: Or, 130 D = 19200; And, D = 147-9/13.

Who can solve the following problem?

A hundred and one by fifty divide, And next let a cipher be duly applied, And if the result you should rightly divine, You’ll find that the whole makes but one out of nine.

EXPLANATION.—CI, CLI, CLIO (Clio, the muse of history, one of the _nine_ muses).

Suppose the figure to represent railroad tracks, C D and E F being each the length of a car or locomotive, and _a_ and _b_ each representing a car on the track and _c_ representing a locomotive on E F. Now how can the locomotive change the relative position of _a_ and _b_ so that _b_ will be on the track where _a_ is and _a_ will be on the track where _b_ is?

ANSWER.—The locomotive _c_ backs _a_ down and out toward A, then runs over toward B and backs _b_ up on E F, then runs back toward B and goes over toward A, then runs up C E and draws _b_ down on C E, then runs over toward A and gets car _a_, draws it over toward B and backs it up on D E. It can also be readily done by first backing _a_ down on A C and drawing to and leaving it on C D.

TALKS

BY GEORGE THATCHER

The Celebrated Minstrel

140 Pages Paper Binding 25 Cents

This unique volume supplies in a most satisfactory way the want that has heretofore been but indifferently met by the so-called Stump-Speech books. Mr. Thatcher is without doubt the most popular man in minstrelsy, his name being known among mirth-loving people everywhere, not only in America, but beyond the seas. It is most fortunate that the services of a person so distinguished have been secured for the preparation of this book, especially since he has put in it his own original matter exactly as he uses it nightly to convulse his audiences with laughter. The book contains all his Monologues, Parodies, Songs, Sketches, Poems, Speeches, Jokes, etc., etc. It will be found invaluable to every humorous reader, to amateur and professional minstrels, and in addition will prove interesting reading to any person who is fond of the lighter vein of literature.

JOKES

GATHERED BY

HENRY FIRTH WOOD

The Popular Humorist

ILLUSTRATED

150 Pages Paper Binding 25 Cents

This attractive little volume is a collection of the brightest, funniest, and most catchy Jokes of the day. They are all short, some of them occupying only six or eight lines, but they are as pointed as short, and all are fairly bristling with wit and humor of the keenest kind. There are no old ones among them, the collection being the very latest crop.

They are classified, according to their character, under such headings as “Womankind,” “Youth,” “Bald and Tough,” etc., ten sections in all, and each headed with a peculiarly appropriate illustration.

The author is widely and favorably known through his humorous lectures and readings, and both publicly and privately is recognized as one of the genuinely funny men of the day.

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The suggestive and peculiarly fitting title of this attractive volume faithfully describes the character of its contents, as it is packed full of fun from the beginning to the end. It is composed of three popular titles, TALKS, by the celebrated minstrel, George Thatcher, containing all his monologues, songs, witty sayings, etc.; JOKES, by the popular humorist, Henry Firth Wood, comprising a multitude of bright and bristling comicalities; and CONUNDRUMS, by Dean Rivers, embracing the latest and best in the line of Conundrums, Riddles, and Puzzles, and including also a number of most complex Arithmetical Puzzles. The different authors and compilers are deservedly popular and prominent as representing the keenest and freshest in everything that is bright and witty, and are a sure guaranty that the volume possesses all the merit that is claimed for it.

The collection as a whole will afford excellent amusement for the fireside, will prove a splendid store-house from which to draw material for anecdote or illustration, is valuable for public reading or entertainment, and will be found enjoyable reading for private perusal, while as a cure for an attack of the blues it is unfailing.

Sold by all Booksellers, or sent, prepaid, upon receipt of price

DANCING

By Marguerite Wilson

A complete instructor, beginning with the first positions and steps and leading up to the square and round dances. It contains also a full list of calls for all of the square dances, and the necessary music for each figure, the etiquette of the dances, and 100 figures for the german. It is unusually well illustrated by a large number of original drawings. Without doubt the best book on the subject.

PRACTICAL PALMISTRY

By Henry Frith

There is to-day probably no more popular character study than that of Palmistry. Many more people would be interested in it if there were a convenient book that came within their comprehension and that was reliable. This volume furnishes full and trustworthy information on the subject, and with a little practice any person will be able to read character, recall past events, and forecast future occurrences, upon examination of the hand. Fully illustrated.

THE PENN PUBLISHING COMPANY 923 Arch Street, Philadelphia

TRANSCRIBER’S NOTE

WARNING: Some of the puns may contain elements that we would today deem stereotyping by race, ethnicity or gender.

Punctuation has been normalized. Variations in hyphenation have been retained as they were in the original publication. The following changes have been made:

draws and colors beatifully —> beautifully {43} vingt quatre —> vingt-quatre {133} cerque —> cirque {133} difference —> différence {133} parse qu’el —> parce qu’il {133} Carthagenois —> Carthaginois {133} Romans —> Romains {133}

Quand un gant resemble-t-il an numero vingt cinq. —> Quand un gant ressemble-t-il au numéro vingt-cinq. {134}

treeze —> treize {134} Un felon peut-il prendu —> Un félon peut-il prendre {134} j’etais —> j’étais {134} que je suis —> ce que je suis {134} maitresse —> maîtresse {134} Je ne suis par —> Je ne suis pas {134} in the margin of —> below {140, ind} in the margin —> below {148, 149 - 3 instances} divide the result by 6, add 25 —> add 20 {141}

The following arithmetic problem in the original publication did not contain a solution:

“Suppose it were possible for a man in Cincinnati to start on Sunday noon,” {page 145}

Repeated chapter headings have been reduced.

Italicized phrases are presented by surrounding the text with _underscores_.

Decorative use of letterspacing has not been represented in this version of the book.

Words and phrases presented using mixed small capital in the original are presented in this version using all capital letters.

Superscripted characters are indicated by preceding them with a caret (^), as here: 3^3 - 3 = 24.

End of Project Gutenberg's Conundrums, Riddles and Puzzles, by Dean Rivers