VARIOUS ARITHMETICAL AND ALGEBRAICAL PROBLEMS.

    “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 extreme edge.

[Illustration]

“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.

98.—­ACADEMIC COURTESIES.

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.

99.—­THE THIRTY-THREE PEARLS.

[Illustration]

“A man I know,” said Teddy Nicholson at a certain family party, “possesses a string of thirty-three pearls.  The middle pearl is the largest and best of all, and the others are so selected and arranged that, starting from one end, each successive pearl is worth L100 more than the preceding one, right up to the big pearl.  From the other end the pearls increase in value by L150 up to the large pearl.  The whole string is worth L65,000.  What is the value of that large pearl?”

“Pearls and other articles of clothing,” said Uncle Walter, when the price of the precious gem had been discovered, “remind me of Adam and Eve.  Authorities, you may not know, differ as to the number of apples that were eaten by Adam and Eve.  It is the opinion of some that Eve 8 (ate) and Adam 2 (too), a total of 10 only.  But certain mathematicians have figured it out differently, and hold that Eve 8 and Adam a total of 16.  Yet the most recent investigators think the above figures entirely wrong, for if Eve 8 and Adam 8 2, the total must be 90.”

“Well,” said Harry, “it seems to me that if there were giants in those days, probably Eve 8 1 and Adam 8 2, which would give a total of 163.”

“I am not at all satisfied,” said Maud.  “It seems to me that if Eve 8 1 and Adam 8 1 2, they together consumed 893.”