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Amusements in Mathematics

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.
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
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
"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."