Amusements in Mathematics, Henry Ernest Dudeney

  • Question 51 - HOW OLD WAS MARY?

    Here is a funny little age problem, by the late Sam Loyd, which has been very popular in the United States. Can you unravel the mystery?The combined ages of Mary and Ann are forty-four years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann. How old is Mary? That is all, but can you work it out? If not, ask your friends to help you, and watch the shadow of bewilderment creep over their faces as they attempt to grip the intricacies of the question.

  • Question 52 - QUEER RELATIONSHIPS

    "Speaking of relationships," said the Parson at a certain dinner-party, "our legislators are getting the marriage law into a frightful tangle, Here, for example, is a puzzling case that has come under my notice. Two brothers married two sisters. One man died and the other man's wife also died. Then the survivors married."

    "The man married his deceased wife's sister under the recent Act?" put in the Lawyer.

    "Exactly. And therefore, under the civil law, he is legally married and his child is legitimate. But, you see, the man is the woman's deceased husband's brother, and therefore, also under the civil law, she is not married to him and her child is illegitimate."

    "He is married to her and she is not married to him!" said the Doctor.

    "Quite so. And the child is the legitimate son of his father, but the illegitimate son of his mother."

    "Undoubtedly 'the law is a hass,'" the Artist exclaimed, "if I may be permitted to say so," he added, with a bow to the Lawyer.

    "Certainly," was the reply. "We lawyers try our best to break in the beast to the service of man. Our legislators are responsible for the breed."

    "And this reminds me," went on the Parson, "of a man in my parish who married the sister of his widow. This man——"

    "Stop a moment, sir," said the Professor. "Married the sister of his widow? Do you marry dead men in your parish?"

    "No; but I will explain that later. Well, this man has a sister of his own. Their names are Stephen Brown and Jane Brown. Last week a young fellow turned up whom Stephen introduced to me as his nephew. Naturally, I spoke of Jane as his aunt, but, to my astonishment, the youth corrected me, assuring me that, though he was the nephew of Stephen, he was not the nephew of Jane, the sister of Stephen. This perplexed me a good deal, but it is quite correct."

    The Lawyer was the first to get at the heart of the mystery. What was his solution?

  • Question 53 - HEARD ON THE TUBE RAILWAY

    First Lady: "And was he related to you, dear?"

    Second Lady: "Oh, yes. You see, that gentleman's mother was my mother's mother-in-law, but he is not on speaking terms with my papa."

    First Lady: "Oh, indeed!" (But you could see that she was not much wiser.)

    How was the gentleman related to the Second Lady?

  • Question 54 - A FAMILY PARTY

    A certain family party consisted of `1` grandfather, `1` grandmother, `2` fathers, `2` mothers, `4` children, `3` grandchildren, `1` brother, `2` sisters, `2` sons, `2` daughters, `1` father-in-law, `1` mother-in-law, and `1` daughter-in-law. Twenty-three people, you will say. No; there were only seven persons present. Can you show how this might be?

  • Question 55 - A MIXED PEDIGREE

    Joseph Bloggs: "I can't follow it, my dear boy. It makes me dizzy!"

    John Snoggs: "It's very simple. Listen again! You happen to be my father's brother-in-law, my brother's father-in-law, and also my father-in-law's brother. You see, my father was——"

    But Mr. Bloggs refused to hear any more. Can the reader show how this extraordinary triple relationship might have come about?

  • Question 56 - WILSON'S POSER

    "Speaking of perplexities——" said Mr. Wilson, throwing down a magazine on the table in the commercial room of the Railway Hotel.

    "Who was speaking of perplexities?" inquired Mr. Stubbs.

    "Well, then, reading about them, if you want to be exact—it just occurred to me that perhaps you three men may be interested in a little matter connected with myself."

    It was Christmas Eve, and the four commercial travellers were spending the holiday at Grassminster. Probably each suspected that the others had no homes, and perhaps each was conscious of the fact that he was in that predicament himself. In any case they seemed to be perfectly comfortable, and as they drew round the cheerful fire the conversation became general.

    "What is the difficulty?" asked Mr. Packhurst.

    "There's no difficulty in the matter, when you rightly understand it. It is like this. A man named Parker had a flying-machine that would carry two. He was a venturesome sort of chap—reckless, I should call him—and he had some bother in finding a man willing to risk his life in making an ascent with him. However, an uncle of mine thought he would chance it, and one fine morning he took his seat in the machine and she started off well. When they were up about a thousand feet, my nephew suddenly——"

    "Here, stop, Wilson! What was your nephew doing there? You said your uncle," interrupted Mr. Stubbs.

    "Did I? Well, it does not matter. My nephew suddenly turned to Parker and said that the engine wasn't running well, so Parker called out to my uncle——"

    "Look here," broke in Mr. Waterson, "we are getting mixed. Was it your uncle or your nephew? Let's have it one way or the other."

    "What I said is quite right. Parker called out to my uncle to do something or other, when my nephew——"

    "There you are again, Wilson," cried Mr. Stubbs; "once for all, are we to understand that both your uncle and your nephew were on the machine?"

    "Certainly. I thought I made that clear. Where was I? Well, my nephew shouted back to Parker——"

    "Phew! I'm sorry to interrupt you again, Wilson, but we can't get on like this. Is it true that the machine would only carry two?"

    "Of course. I said at the start that it only carried two."

    "Then what in the name of aerostation do you mean by saying that there were three persons on board?" shouted Mr. Stubbs.

    "Who said there were three?"

    "You have told us that Parker, your uncle, and your nephew went up on this blessed flying-machine."

    "That's right."

    "And the thing would only carry two!"

    "Right again."

    "Wilson, I have known you for some time as a truthful man and a temperate man," said Mr. Stubbs, solemnly. "But I am afraid since you took up that new line of goods you have overworked yourself."

    "Half a minute, Stubbs," interposed Mr. Waterson. "I see clearly where we all slipped a cog. Of course, Wilson, you meant us to understand that Parker is either your uncle or your nephew. Now we shall be all right if you will just tell us whether Parker is your uncle or nephew."

    "He is no relation to me whatever."

    The three men sighed and looked anxiously at one another. Mr. Stubbs got up from his chair to reach the matches, Mr. Packhurst proceeded to wind up his watch, and Mr. Waterson took up the poker to attend to the fire. It was an awkward moment, for at the season of goodwill nobody wished to tell Mr. Wilson exactly what was in his mind.

    "It's curious," said Mr. Wilson, very deliberately, "and it's rather sad, how thick-headed some people are. You don't seem to grip the facts. It never seems to have occurred to either of you that my uncle and my nephew are one and the same man."

    "What!" exclaimed all three together.

    "Yes; David George Linklater is my uncle, and he is also my nephew. Consequently, I am both his uncle and nephew. Queer, isn't it? I'll explain how it comes about.

    "Mr. Wilson put the case so very simply that the three men saw how it might happen without any marriage within the prohibited degrees. Perhaps the reader can work it out for himself.

  • Question 57 - WHAT WAS THE TIME?

    "I say, Rackbrane, what is the time?" an acquaintance asked our friend the professor the other day. The answer was certainly curious.

    "If you add one quarter of the time from noon till now to half the time from now till noon to-morrow, you will get the time exactly."

    What was the time of day when the professor spoke?

  • Question 58 - A TIME PUZZLE

    How many minutes is it until six o'clock if fifty minutes ago it was four times as many minutes past three o'clock?

  • Question 59 - A PUZZLING WATCH

    A friend pulled out his watch and said, "This watch of mine does not keep perfect time; I must have it seen to. I have noticed that the minute hand and the hour hand are exactly together every sixty-five minutes." Does that watch gain or lose, and how much per hour?

  • Question 60 - THE WAPSHAW'S WHARF MYSTERY

    There was a great commotion in Lower Thames Street on the morning of January `12, 1887`. When the early members of the staff arrived at Wapshaw's Wharf they found that the safe had been broken open, a considerable sum of money removed, and the offices left in great disorder. The night watchman was nowhere to be found, but nobody who had been acquainted with him for one moment suspected him to be guilty of the robbery. In this belief the proprietors were confirmed when, later in the day, they were informed that the poor fellow's body had been picked up by the River Police. Certain marks of violence pointed to the fact that he had been brutally attacked and thrown into the river. A watch found in his pocket had stopped, as is invariably the case in such circumstances, and this was a valuable clue to the time of the outrage. But a very stupid officer (and we invariably find one or two stupid individuals in the most intelligent bodies of men) had actually amused himself by turning the hands round and round, trying to set the watch going again. After he had been severely reprimanded for this serious indiscretion, he was asked whether he could remember the time that was indicated by the watch when found. He replied that he could not, but he recollected that the hour hand and minute hand were exactly together, one above the other, and the second hand had just passed the forty-ninth second. More than this he could not remember.

    What was the exact time at which the watchman's watch stopped? The watch is, of course, assumed to have been an accurate one.