Henry Ernest Dudeney/Puzzles and Curious Problems/Arithmetical and Algebraical Problems/Age and Kinship Puzzles
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Henry Ernest Dudeney: Puzzles and Curious Problems: Arithmetical and Algebraical Problems
$38$ - The Picnic
- Four married couples had a picnic together, and their refreshments included $32$ bottles of lemonade.
- Mary only disposed of one bottle,
- Anne had two,
- Jane swallowed the contents of three,
- and Elizabeth emptied four bottles.
- The husbands were more thirsty,
- except John MacGregor, who drank the same quantity as his better half.
- Lloyd Jones drank twice as much as his wife,
- William Smith three times as much as his wife,
- and Patrick Dolan four times as much as his wife demanded.
- The puzzle is to find the surnames of the ladies.
- Which man was married to which woman?
$39$ - Surprising Relationship
- Angelina: "You say that Mr. Tomkins is your uncle?"
- Edwin: "Yes, and I am his uncle!"
- Angelina: Then -- let me see -- you must be nephew to each other, of course! Funny, isn't it?"
- Can you say quite simply how this might be, without any breach of the marriage law or disregard of the Table of Affinity?
$40$ - An Epitaph (A.D. $1538$)
- Two grandmothers, with their two granddaughters;
- Two husbands, with their two wives;
- Two fathers, with their two daughters;
- Two mothers, with their two sons;
- Two maidens, with their two mothers;
- Two sisters, with their two brothers;
- Yet only six in all lie buried here;
- All born legitimate, from incest clear.
- How might this happen?
$41$ - Ancient Problem
- Demochares has lived one-fourth of his life as a boy;
- one-fifth as a youth;
- one-third as a man;
- and has spent thirteen years in his dotage.
- How old is this gentleman?
$42$ - Family Ages
- A man and his wife had three children, John, Ben, and Mary,
- and the difference between their parents' ages was the same as between John and Ben and between Ben and Mary.
- The ages of John and Ben, multiplied together, equalled the age of the father,
- and the ages of Ben and Mary multiplied together equalled the age of the mother.
- The combined ages of the family amounted to ninety years.
- What was the age of each person?
$43$ - Mike's Age
- Pat O'Connor is $1 \tfrac 1 3$ times as old as when he built the pigsty.
- Little Mike, who was $40$ months old when Pat built the sty, is now two years more than half as old as Pat's wife, Biddy, was when Pat built the sty,
- so that when Little Mike is as old as Pat was when he built the sty,
- their three ages combined will amount to just one hundred years.
- How old is Little Mike?
$44$ - Their Ages
- A man, on being asked the ages of his two sons, stated that
- eighteen more than the sum of their ages is double the age of the elder,
- and six less than the difference of their ages is the age of the younger.
- What are their ages?
$45$ - Brother and Sister
- A boy on being asked the age of himself and his sister replied:
- "Three years ago I was seven times as old as my sister;
- two years ago I was four times as old;
- last year I was three times as old;
- and this year I am two and one-half times as old."
- What are their ages?
$46$ - A Square Family
- A man had nine children, all born at regular intervals,
- and the sum of the squares of their ages was equal to the square of his own.
- What were the ages of each?
- Every age was an exact number of years.
$47$ - The Quarrelsome Children
- A man married a widow, and they each already had children.
- Ten years later there was a pitched battle engaging the present family of $12$ children.
- The mother ran to the father and cried,
- "Come at once! Your children and my children are fighting our children!"
- As the parents now had each nine children of their own, how many were born during the ten years?
$48$ - Robinson's Age
- Robinson said.
- My brother is two years older than I,
- my sister is four years older than he,
- my mother was $20$ when I was born,
- and I was told yesterday that the average age of the four of is is $39$ years.
- What was Robinson's age?
$49$ - The Engine-Driver's Name
- Three business men -- Smith, Robinson and Jones -- all live in the Leeds-Sheffield district.
- Three railwaymen of similar names live in the same district.
- The business man Robinson and the guard live at Sheffield,
- the business man Jones and the stoker live at Leeds,
- while the business man Smith and the engine-driver live half-way between Leeds and Sheffield.
- The guard's namesake earns $\pounds 1000, 10 \shillings 2 \oldpence$ per annum,
- and the engine-driver earns exactly one-third of the business man living nearest to him.
- Finally, the railwayman Smith beats the stoker at billiards.
- What is the engine driver's name?
$50$ - Buying Ribbon
- Four mothers, each with one daughter, went into a shop to buy ribbon.
- Each mother bought twice as many yards as her daughter,
- and each person bought as many yards of ribbon as the number of farthings she paid for each yard.
- Mrs. Jones spent $1 \shillings 7 \oldpence$ more than Mrs. White;
- Nora bought three yards less than Mrs. Brown;
- Gladys bought two yards more than Hilda,
- who spent $1 \shillings$ less than Mrs. Smith.
- What is the name of Mary's mother?
$51$ - Sharing the Apples
- Eight children had a basket containing $32$ apples.
- They divided them amongst themselves as follows:
- Anne got one apple,
- Mary two,
- Jane three,
- and Kate four.
- Ned Smith took as many as his sister,
- Tom Brown twice as many as his sister,
- Bill Jones three times as many as his sister,
- and Jack Robinson four times as many as his sister.
- What are the full names of the girls?
$52$ - In the Year $1900$
- A man's age at death was one-twenty-ninth of the year of his birth.
- How old was he in the year $1900$?
$53$ - Finding a Birthday
- A correspondent informs us incidentally that on Armistice Day (Nov. 11, 1928)
- he would have lived as long in the $20$th century as he lived in the $19$th.
- This tempted us to work out the day of his birth.
- Perhaps the reader may like to do the same.
$54$ - The Birth of Boadicea
- Boadicea died $129$ years after Cleopatra was born.
- Their united ages (that is, the combined years of their complete lives) were $100$ years.
- Cleopatra died $\text {30}$ $\text {BCE}$.
- When was Boadicea born?
$55$ - Eliza's Surname
- Smith, Brown and Robinson have provided themselves with a penny pencil each,
- and took their wives to a stockbroker's office to buy shares.
- Mary bought $50$ more shares than Brown,
- and Robinson $120$ more than Jane.
- Each man paid as many shillings per share as he bought shares,
- What was Eliza's surname?