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Note that £1 = 1 pound = 20 shillings = 4 crowns, and 1 shilling = 1s. = 12 pence = 12d. Also 1 penny = 4 farthings. A sovereign is another name for a pound. A guinea is 21 shillings. The gold coins were: sovereign and half-sovereign. The silver coins were: crown, half-crown, florin (= 2s.), a shilling, sixpence, and threepence. The copper coins were: penny, halfpenny and farthing. Readers would also have been familiar with three other silver coins: the double-florin (4s, rare after 1890), the groat (4d, rare after 1855), and the half-groat (2d, rare after 1848).
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1. In every business of life we are occasionally perplexed by some chance question that for the moment staggers us. I quite pitied a young lady in a branch post-office when a gentleman entered and deposited a crown on the counter with this request: "Please give me some twopenny stamps, six times as many penny stamps, and make up the rest of the money in twopence-halfpenny stamps." For a moment she seemed bewildered, then her brain cleared, and with a smile she handed over stamps in exact fulfilment of the order. How long would it have taken you to think it out?
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2. The precocity of some youths is surprising. One is disposed to say on occasion, "That boy of yours is a genius, and he is certain to do great things when he grows up;" but past experience has taught us that he invariably becomes quite an ordinary citizen. It is so often the case, on the contrary, that the dull boy becomes a great man. You never can tell. Nature loves to present to us these queer paradoxes. It is well-known that those wonderful "lightning calculators" who now and again surprise the world by their feats, lose all their mysterious powers directly they are taught the elementary rules of arithmetic.
A boy who was demolishing a choice banana was approached by a young friend, who, regarding him with envious eyes, asked, "How much did you pay for that banana, Fred?" The prompt answer was quite remarkable in its way: "The man what I bought it of receives just half as many sixpences for sixteen dozen dozen bananas as he gives bananas for a fiver."
Now, how long will it take the reader to say correctly just how much Fred paid for his rare and refreshing fruit?
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3. Three countrymen met at a cattle market. "Look here, " said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got." "If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I." "Well, I'll go better than that, " said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here."
No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge and Durrant must have taken to the cattle market.
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4. A number of men went out together on a bean-feast. There were four parties invited - namely, 25 cobblers, 20 tailors, 18 hatters, and 12 glovers. They spent altogether £6, 13s. It was found that five cobblers spent as much as four tailors; that twelve tailors spent as much as nine hatters; and that six hatters spent as much as eight glovers. The puzzle is to find out how much each of the four parties spent.
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5. Seven men, whose names were Adams, Baker, Carter, Dobson, Edwards, Francis and Gudgeon, were recently engaged in play. The name of the particular game is of no consequence. They had agreed that whenever a player won a game he should double the money of each of the other players - that is, he was to give the other players just as much money as they had already in their pockets. They played seven games, and strange to say, each won a game in turn, in the order in which their names are given. But a more curious coincidence is this - that when they had finished play each of the seven men had exactly the same amount - two shillings and eightpence - in his pocket. The puzzle is to find out how much money each had with him before he sat down to play.
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6. A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish; but they were only to continue the gift so long as they could make it in different ways, always giving eighteen pence each to a number of women and half a crown each to men. During how many years could the charity be administered? Of course, by "different ways" is meant a different number of men and women every time.
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7. A gentleman who recently died left the sum of £8,000 to be divided among his widow, five sons, and four daughters. He directed that every son should receive three times as much as a daughter, and that every daughter should have twice as much as their mother. What was the widow's share?
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8. A charitable gentleman, on his way home one night, was appealed to by three needy persons in succession for assistance. To the first person he gave one penny more than half the money he had in his pocket; to the second person he gave twopence more than half the money he then had in his pocket; and to the third person he handed over threepence more than half of what he had left. On entering his house he had only one penny in his pocket. Now, can you say exactly how much money that gentleman had on him when he started for home?
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9. A man recently bought two aeroplanes, but afterwards found that they would not answer the purpose for which he wanted them. So he sold them for £600 each, making a loss of 20 per cent on one machine and a profit of 20 per cent on the other. Did he make a profit on the whole transaction, or a loss? And how much?
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10. "Whom do you think I met in town last week, Brother William?" said Uncle Benjamin. "That old skinflint Jorkins. His family had been taking him around buying Christmas presents. He said to me, 'Why cannot the government abolish Christmas, and make the giving of presents punishable by law? I came out this morning with a certain amount of money in my pocket, and I find I have spent just half of it. In fact, if you will believe me, I take home just as many shillings as I had pounds, and half as many pounds as I had shillings. It is monstrous!' ". Can you say exactly how much money Jorkins had spent on those presents?
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11. 'Twas last Bank Holiday, so I've been told,
Some cyclists rode abroad in glorious weather.
Resting at noon within a tavern old,
They all agreed to have a feast together.
"Put it all in one bill, mine host," they said,
"For every man an equal share will pay."
The bill was promptly on the table laid,
And four pounds was the reckoning that day.
But, sad to state, when they prepared to square,
'Twas found that two had sneaked outside and fled.
So, for two shillings more than his due share
Each honest man who had remained was bled.
They settled later with those rogues, no doubt.
How many were they when they first set out?
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12. It will be found that £66, 6s. 6d equals 15, 918 pence. Now, the four 6's added together make 24, and the figures 15, 918 also add to 24. It is a curious fact that there is only one other sum of money, in pounds, shillings and pence (all similarly repetitions of one figure), of which the digits shall add up the same as the digits of the amount in pence. What is the other sum of money?
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13. The largest sum of money that can be written in pounds, shillings, pence, and farthings, using each of the nine digits once and only once, is £98, 765, 4s. 3 1/2d. Now try to discover the smallest sum of money that can be written down under precisely the same conditions. There must be some value given for each denomination - pounds, shillings, pence and farthings - and the nought may not be used. It requires just a little judgment and thought.
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14. "This is queer, " said McCrank to his friend. "Twopence added to twopence is fourpence, and twopence multiplied by twopence is also fourpence." Of course, he was wrong in thinking you can multiply money by money. The multiplier must be regarded as an abstract number. It is true that two feet multiplied by two feet will make four square feet. Similarly, two pence multiplied by two pence will produce four square pence! And it will perplex the reader to say what a "square penny" is. But we will assume for the purposes of our puzzle that twopence multiplied by twopence is fourpence. Now, what two amounts of money will produce the next smallest possible result, the same in both cases, when added or multiplied in this manner? The two amounts need not be alike, but they must be those that can be paid in current coins of the realm.
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15. What is the largest sum of money - all in current silver coins and no four-shilling piece - that I could have in my pocket without being able to give change for a half-sovereign?
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16. Mr Morgan G Bloomgarten, the millionaire, known in the States as the Clam King, had, for his sins, more money than he knew what to do with. It bored him. So he determined to persecute some of his poor but happy friends with it. They had never done him any harm, but he resolved to inoculate them with the "source of all evil". He therefore proposed to distribute a million dollars among them and watch them go rapidly to the bad. But he as a man of strange fancies and superstitions, and it was an inviolable rule with him never to make a gift that was not either one dollar or some power of seven - such as 7, 49, 343, 2401, which numbers of dollars are produced by simply multiplying sevens together. Another rule of his was that he would never give more than six persons exactly the same sum. Now, how was he to distribute the 1,000,000 dollars? You may distribute the money among as many people as you like, under the conditions given.
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17. Four brothers - named John, William, Charles and Thomas - had each a money-box. They boxes were all given to them on the same day, and they had at once put what money they had into them; only, as the boxes were not very large, they first changed the money into as few coins as possible. After they had done this, they told one another how much money they had saved, and it was found that if John had had 2s more in his box than at present, if William had had 2s less, if Charles had had twice as much, and if Thomas had had half as much, they would all have had exactly the same amount.
Now, when I add that all four boxes together contained 45s, and that there were only six coins in all in them, it becomes an entertaining puzzle to discover just what coins were in each box.
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18. A number of market women sold their various products at a certain price per pound (different in every case), and each received the same amount - 2s. 2 1/4d. What is the greatest number of women there could have been? The price per pound in every case must be such as could be paid in current money.
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19. The proprietor of a small London cafe has given me some interesting figures. He says that the ladies who come alone to his place for refreshment spend each on an average eighteenpence, that the unaccompanied men spend half a crown each, and that when a gentleman brings in a lady he spends half a guinea. On New Year's Eve he supplied suppers to twenty-five persons and took five pounds in all. Now, assuming his averages have held good in every case, how was his company made up on that occasion? Of course, only single gentlemen, single ladies, and pairs (a lady and a gentleman) can be supposed to have been present, as we are not considering larger parties.
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20. "A neighbour of mine," said Aunt Jane, "bought a certain quantity of beef a two shillings a pound, and the same quantity of sausages at eighteenpence a pound. I pointed out to her that if she had divided the same money equally between beef and sausages she would have gained two pounds in the total weight. Can you tell me exactly how much she spent?"
"Of course, it is no business of mine," said Mrs Sunniborne; "but a lady who could pay such prices must be somewhat inexperienced in domestic economy."
"I quite agree, my dear," Aunt Jane replied, "but you see that is not the precise point under discussion, any more than the name and morals of the tradesman."
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21. I paid a man a shilling for some apples, but they were so small that I made him throw in two extra apples. I find that made them cost just a penny a dozen less than the first price he asked. How many apples did I get for my shilling?
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22. A man recently went into a dairyman's shop to buy eggs. He wanted them of various qualities. The salesman had new-laid eggs at the high price of fivepence each, fresh eggs at one penny each, eggs at a halfpenny each, and eggs for electioneering purposes at a greatly reduced figure, but as there was no election on at the time the buyer had no use for the last. However, he bought some of each of the three other kinds and obtained exactly one hundred eggs for eight and fourpence. Now, as he brought away exactly the same number of eggs of two of the three qualities, it is an interesting puzzle to determine just how many he bought at each price.
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23. Some years ago a man told me he had spent one hundred English silver coins in Christmas-boxes, giving every person the same amount, and it cost him exactly £1, 10s 1d. Can you tell just how many persons received the present, and how he could have managed the distribution? That odd penny looks queer, but it is all right.
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24. Two ladies went into a shop, where, through some curious eccentricity, no change was given, and made purchases amounting together to less than five shillings. "Do you know," said one lady, "I find I shall require no fewer than six current coins of the realm to pay for what I have bought." The other lady considered a moment, and then exclaimed: "By a peculiar coincidence, I am exactly in the same dilemma." "Then we will pay the two bills together." But, to their astonishment, they still required six coins. What is the smallest possible amount of their purchases - both different?
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25. The Chinese are a curious people, and have strange inverted ways of doing things. It is said that they use a saw with an upward pressure instead of a downward one, that they plane a deal board by pulling the tool toward them instead of pushing it, and that in building a house they first construct the roof and, having raised that into position, proceed to work downwards. In money the currency of the country consists of taels of fluctuating value. The tael became thinner and thinner until 2000 of them piled together made less than three inches in height. The common cash consists of brass coins of varying thickness, with a round, square, or triangular hold in the center. These are strung on wires like buttons. Supposing that eleven coins with round holes are worth fifteen ching-changs, that eleven with square holes are worth sixteen ching-changs, and that eleven with triangular holes are worth seventeen ching-changs, how can a Chinaman give me change for half a crown, using no coins other than the three mentioned? A ching-chang is worth exactly twopence and four-fifteenths of a ching-chang.
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Originally copyright by H E Dudeney (died 1930). Now out of copyright.
