Mathematics Puzzles On Algebra

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.



"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.


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.


THE THIRTY-THREE PEARLS.



"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."

"I am sure you are all wrong," insisted Mr. Wilson, "for I consider that
Eve 8 1 4 Adam, and Adam 8 1 2 4 Eve, so we get a total of 8,938."

"But, look here," broke in Herbert. "If Eve 8 1 4 Adam and Adam 8 1 2 4
2 oblige Eve, surely the total must have been 82,056!"

At this point Uncle Walter suggested that they might let the matter
rest. He declared it to be clearly what mathematicians call an
indeterminate problem.


THE LABOURER'S PUZZLE.

Professor Rackbrane, during one of his rambles, chanced to come upon a
man digging a deep hole.

"Good morning," he said. "How deep is that hole?"

"Guess," replied the labourer. "My height is exactly five feet ten
inches."

"How much deeper are you going?" said the professor.

"I am going twice as deep," was the answer, "and then my head will be
twice as far below ground as it is now above ground."

Rackbrane now asks if you could tell how deep that hole would be when
finished.


THE TRUSSES OF HAY.

Farmer Tompkins had five trusses of hay, which he told his man Hodge to
weigh before delivering them to a customer. The stupid fellow weighed
them two at a time in all possible ways, and informed his master that
the weights in pounds were 110, 112, 113, 114, 115, 116, 117, 118, 120,
and 121. Now, how was Farmer Tompkins to find out from these figures how
much every one of the five trusses weighed singly? The reader may at
first think that he ought to be told "which pair is which pair," or
something of that sort, but it is quite unnecessary. Can you give the
five correct weights?


MR. GUBBINS IN A FOG.

Mr. Gubbins, a diligent man of business, was much inconvenienced by a
London fog. The electric light happened to be out of order and he had to
manage as best he could with two candles. His clerk assured him that
though both were of the same length one candle would burn for four hours
and the other for five hours. After he had been working some time he put
the candles out as the fog had lifted, and he then noticed that what
remained of one candle was exactly four times the length of what was
left of the other.

When he got home that night Mr. Gubbins, who liked a good puzzle, said
to himself, "Of course it is possible to work out just how long those
two candles were burning to-day. I'll have a shot at it." But he soon
found himself in a worse fog than the atmospheric one. Could you have
assisted him in his dilemma? How long were the candles burning?

Read more articles on mathematics and math puzzles at my blog www.mathtutoronline.blogspot.com and
www.articlesoneducation.blogspot.com