Amusements in Mathematics, Henry Ernest Dudeney

  • Question 31 - DOMESTIC ECONOMY

    Young Mrs. Perkins, of Putney, writes to me as follows: "I should be very glad if you could give me the answer to a little sum that has been worrying me a good deal lately. Here it is: We have only been married a short time, and now, at the end of two years from the time when we set up housekeeping, my husband tells me that he finds we have spent a third of his yearly income in rent, rates, and taxes, one-half in domestic expenses, and one-ninth in other ways. He has a balance of £`190` remaining in the bank. I know this last, because he accidentally left out his pass-book the other day, and I peeped into it. Don't you think that a husband ought to give his wife his entire confidence in his money matters? Well, I do; and—will you believe it?—he has never told me what his income really is, and I want, very naturally, to find out. Can you tell me what it is from the figures I have given you?"

    Yes; the answer can certainly be given from the figures contained in Mrs. Perkins's letter. And my readers, if not warned, will be practically unanimous in declaring the income to be—something absurdly in excess of the correct answer!

  • Question 32 - THE EXCURSION TICKET PUZZLE

    When the big flaming placards were exhibited at the little provincial railway station, announcing that the Great —— Company would run cheap excursion trains to London for the Christmas holidays, the inhabitants of Mudley-cum-Turmits were in quite a flutter of excitement. Half an hour before the train came in the little booking office was crowded with country passengers, all bent on visiting their friends in the great Metropolis. The booking clerk was unaccustomed to dealing with crowds of such a dimension, and he told me afterwards, while wiping his manly brow, that what caused him so much trouble was the fact that these rustics paid their fares in such a lot of small money.

    He said that he had enough farthings to supply a West End draper with change for a week, and a sufficient number of threepenny pieces for the congregations of three parish churches. "That excursion fare," said he, "is nineteen shillings and ninepence, and I should like to know in just how many different ways it is possible for such an amount to be paid in the current coin of this realm."

    Here, then, is a puzzle: In how many different ways may nineteen shillings and ninepence be paid in our current coin? Remember that the fourpenny-piece is not now current.

    Topics:
    Combinatorics

  • Question 33 - A PUZZLE IN REVERSALS

    Most people know that if you take any sum of money in pounds, shillings, and pence, in which the number of pounds (less than £`12`) exceeds that of the pence, reverse it (calling the pounds pence and the pence pounds), find the difference, then reverse and add this difference, the result is always £`12, 18`s. `11`d. But if we omit the condition, "less than £`12`," and allow nought to represent shillings or pence—(`1`) What is the lowest amount to which the rule will not apply? (`2`) What is the highest amount to which it will apply? Of course, when reversing such a sum as £`14, 15`s. `3`d. it may be written £`3, 16`s. `2`d., which is the same as £`3, 15`s. `14`d.

  • Question 34 - THE GROCER AND DRAPER

    A country "grocer and draper" had two rival assistants, who prided themselves on their rapidity in serving customers. The young man on the grocery side could weigh up two one-pound parcels of sugar per minute, while the drapery assistant could cut three one-yard lengths of cloth in the same time. Their employer, one slack day, set them a race, giving the grocer a barrel of sugar and telling him to weigh up forty-eight one-pound parcels of sugar While the draper divided a roll of forty-eight yards of cloth into yard pieces. The two men were interrupted together by customers for nine minutes, but the draper was disturbed seventeen times as long as the grocer. What was the result of the race?

  • Question 35 - JUDKINS'S CATTLE

    Hiram B. Judkins, a cattle-dealer of Texas, had five droves of animals, consisting of oxen, pigs, and sheep, with the same number of animals in each drove. One morning he sold all that he had to eight dealers. Each dealer bought the same number of animals, paying seventeen dollars for each ox, four dollars for each pig, and two dollars for each sheep; and Hiram received in all three hundred and one dollars. What is the greatest number of animals he could have had? And how many would there be of each kind?

  • Question 36 - BUYING APPLES

    As the purchase of apples in small quantities has always presented considerable difficulties, I think it well to offer a few remarks on this subject. We all know the story of the smart boy who, on being told by the old woman that she was selling her apples at four for threepence, said: "Let me see! Four for threepence; that's three for twopence, two for a penny, one for nothing—I'll take one!"

    There are similar cases of perplexity. For example, a boy once picked up a penny apple from a stall, but when he learnt that the woman's pears were the same price he exchanged it, and was about to walk off. "Stop!" said the woman. "You haven't paid me for the pear!" "No," said the boy, "of course not. I gave you the apple for it." "But you didn't pay for the apple!" "Bless the woman! You don't expect me to pay for the apple and the pear too!" And before the poor creature could get out of the tangle the boy had disappeared.

    Then, again, we have the case of the man who gave a boy sixpence and promised to repeat the gift as soon as the youngster had made it into ninepence. Five minutes later the boy returned. "I have made it into ninepence," he said, at the same time handing his benefactor threepence. "How do you make that out?" he was asked. "I bought threepennyworth of apples." "But that does not make it into ninepence!" "I should rather think it did," was the boy's reply. "The apple woman has threepence, hasn't she? Very well, I have threepennyworth of apples, and I have just given you the other threepence. What's that but ninepence?"

    I cite these cases just to show that the small boy really stands in need of a little instruction in the art of buying apples. So I will give a simple poser dealing with this branch of commerce.

    An old woman had apples of three sizes for sale—one a penny, two a penny, and three a penny. Of course two of the second size and three of the third size were respectively equal to one apple of the largest size. Now, a gentleman who had an equal number of boys and girls gave his children sevenpence to be spent amongst them all on these apples. The puzzle is to give each child an equal distribution of apples. How was the sevenpence spent, and how many children were there?

    Topics:
    Algebra -> Word Problems

  • Question 37 - BUYING CHESTNUTS

    Though the following little puzzle deals with the purchase of chestnuts, it is not itself of the "chestnut" type. It is quite new. At first sight it has certainly the appearance of being of the "nonsense puzzle" character, but it is all right when properly considered.

    A man went to a shop to buy chestnuts. He said he wanted a pennyworth, and was given five chestnuts. "It is not enough; I ought to have a sixth," he remarked! "But if I give you one chestnut more." the shopman replied, "you will have five too many." Now, strange to say, they were both right. How many chestnuts should the buyer receive for half a crown?

  • Question 38 - THE BICYCLE THIEF

    Here is a little tangle that is perpetually cropping up in various guises. A cyclist bought a bicycle for £`15` and gave in payment a cheque for £`25`. The seller went to a neighbouring shopkeeper and got him to change the cheque for him, and the cyclist, having received his £`10` change, mounted the machine and disappeared. The cheque proved to be valueless, and the salesman was requested by his neighbour to refund the amount he had received. To do this, he was compelled to borrow the £`25` from a friend, as the cyclist forgot to leave his address, and could not be found. Now, as the bicycle cost the salesman £`11`, how much money did he lose altogether?

    Topics:
    Algebra -> Word Problems

  • Question 39 - THE COSTERMONGER'S PUZZLE

    "How much did yer pay for them oranges, Bill?"

    "I ain't a-goin' to tell yer, Jim. But I beat the old cove down fourpence a hundred."

    "What good did that do yer?"

    "Well, it meant five more oranges on every ten shillin's-worth."

    Now, what price did Bill actually pay for the oranges? There is only one rate that will fit in with his statements.

  • Question 40 - MAMMA'S AGE

    Tommy: "How old are you, mamma?"

    Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."

    Tommy: "That's a lot, isn't it? And how old are you, papa?"

    Papa: "Just six times as old as you, my son."

    Tommy: "Shall I ever be half as old as you, papa?"

    Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."

    Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing——"

    Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."

    Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?