Amusements in Mathematics
I have a set of four dice, not marked with spots in the ordinary way, but with Arabic
figures, as shown in the illustration. Each die, of course, bears the numbers 1 to 6. When
put together they will form a good many, different numbers. As represented they make
the number 1246. Now, if I make all the different four-figure numbers that are possible
with these dice (never putting the same figure more than once in any number), what will
they all add up to? You are allowed to turn the 6 upside down, so as to represent a 9. I do
not ask, or expect, the reader to go to all the labour of writing out the full list of numbers
and then adding them up. Life is not long enough for such wasted energy. Can you get at
the answer in any other way?
VARIOUS ARITHMETICAL AND ALGEBRAICAL
"Variety's the very spice of life,
That gives it all its flavour."
COWPER: The Task.
97.—THE SPOT ON THE TABLE.
A boy, recently home from school, wished to give his father an exhibition of his
precocity. He pushed a large circular table into the corner of the room, as shown in the
illustration, so that it touched both walls, and he then pointed to a spot of ink on the
"Here is a little puzzle for you, pater," said the youth. "That spot is exactly eight inches
from one wall and nine inches from the other. Can you tell me the diameter of the table
without measuring it?"
The boy was overheard to tell a friend, "It fairly beat the guv'nor;" but his father is known
to have remarked to a City acquaintance that he solved the thing in his head in a minute. I
often wonder which spoke the truth.
In a certain mixed school, where a special feature was made of the inculcation of good
manners, they had a curious rule on assembling every morning. There were twice as
many girls as boys. Every girl made a bow to every other girl, to every boy, and to the
teacher. Every boy made a bow to every other boy, to every girl, and to the teacher. In all
there were nine hundred bows made in that model academy every morning. Now, can you
say exactly how many boys there were in the school? If you are not very careful, you are
likely to get a good deal out in your calculation.