Henry Ernest Dudeney/Puzzles and Curious Problems/Arithmetical and Algebraical Problems/Age and Kinship Puzzles

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,

and each wife as many pence per share as she bought shares,

and every man spent one guinea more than his wife.

What was Eliza's surname?