Amusements in Mathematics | Page 9

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?

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?
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.

AGE AND KINSHIP PUZZLES.
"The days of our years are threescore years and ten."
--Psalm xc. 10.
For centuries it has been a favourite method of propounding arithmetical puzzles to pose
them in the form of questions as to the age of an individual. They generally lend
themselves to very easy solution by the use of algebra, though often the difficulty lies in
stating them correctly. They may be made very complex and may demand considerable
ingenuity, but no general laws can well be laid down for their solution. The solver must
use his own sagacity. As for puzzles in relationship or kinship, it is quite curious how
bewildering many people find these things. Even in ordinary conversation, some
statement as to relationship, which is quite clear in the mind of the speaker, will
immediately tie the brains of other people into knots. Such expressions as "He is my
uncle's son-in-law's sister" convey absolutely nothing to some people without a detailed
and laboured explanation. In such cases the best course is to sketch a brief genealogical
table, when the eye comes immediately to the assistance of the brain. In these days, when
we have a growing lack of respect for pedigrees, most people have got out of the habit of
rapidly drawing such tables, which is to be regretted, as they would save a lot of time and
brain racking on occasions.
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?
41.--THEIR AGES.
"My husband's age," remarked a lady the other day, "is represented by the figures of my
own age reversed. He is my senior, and the difference between our ages is one-eleventh
of their sum."
42.--THE FAMILY AGES.
When the Smileys recently received a visit from the favourite uncle, the fond parents had
all the five children brought into his presence. First came Billie and little Gertrude, and
the uncle was informed that the boy was exactly twice as old as the girl. Then Henrietta
arrived, and it was pointed out that the combined ages of herself and Gertrude equalled
twice the age of Billie. Then Charlie came running in, and somebody remarked that now
the combined ages of the two boys were exactly twice the combined ages of the two girls.
The uncle was expressing his astonishment at these coincidences when Janet came in.
"Ah! uncle," she