Amusements in Mathematics | Page 5

to do with. It bored him. So he determined to
persecute some of his poor but happy friends with it. They had never done him any harm,
but he resolved to inoculate them with the "source of all evil." He therefore proposed to
distribute a million dollars among them and watch them go rapidly to the bad. But he was
a man of strange fancies and superstitions, and it was an inviolable rule with him never to
make a gift that was not either one dollar or some power of seven--such as 7, 49, 343,
2,401, which numbers of dollars are produced by simply multiplying sevens together.
Another rule of his was that he would never give more than six persons exactly the same
sum. Now, how was he to distribute the 1,000,000 dollars? You may distribute the money

among as many people as you like, under the conditions given.
17.--THE PUZZLING MONEY-BOXES.
Four brothers--named John, William, Charles, and Thomas--had each a money-box. The
boxes were all given to them on the same day, and they at once put what money they had
into them; only, as the boxes were not very large, they first changed the money into as
few coins as possible. After they had done this, they told one another how much money
they had saved, and it was found that if John had had 2s. more in his box than at present,
if William had had 2s. less, if Charles had had twice as much, and if Thomas had had half
as much, they would all have had exactly the same amount.
Now, when I add that all four boxes together contained 45s., and that there were only six
coins in all in them, it becomes an entertaining puzzle to discover just what coins were in
each box.
18.--THE MARKET WOMEN.
A number of market women sold their various products at a certain price per pound
(different in every case), and each received the same amount--2s. 2½d. What is the
greatest number of women there could have been? The price per pound in every case
must be such as could be paid in current money.
19.--THE NEW YEAR'S EVE SUPPERS.
The proprietor of a small London café has given me some interesting figures. He says
that the ladies who come alone to his place for refreshment spend each on an average
eighteenpence, that the unaccompanied men spend half a crown each, and that when a
gentleman brings in a lady he spends half a guinea. On New Year's Eve he supplied
suppers to twenty-five persons, and took five pounds in all. Now, assuming his averages
to have held good in every case, how was his company made up on that occasion? Of
course, only single gentlemen, single ladies, and pairs (a lady and gentleman) can be
supposed to have been present, as we are not considering larger parties.
20.--BEEF AND SAUSAGES.
"A neighbour of mine," said Aunt Jane, "bought a certain quantity of beef at two shillings
a pound, and the same quantity of sausages at eighteenpence a pound. I pointed out to her
that if she had divided the same money equally between beef and sausages she would
have gained two pounds in the total weight. Can you tell me exactly how much she
spent?"
"Of course, it is no business of mine," said Mrs. Sunniborne; "but a lady who could pay
such prices must be somewhat inexperienced in domestic economy."
"I quite agree, my dear," Aunt Jane replied, "but you see that is not the precise point
under discussion, any more than the name and morals of the tradesman."

21.--A DEAL IN APPLES.
I paid a man a shilling for some apples, but they were so small that I made him throw in
two extra apples. I find that made them cost just a penny a dozen less than the first price
he asked. How many apples did I get for my shilling?
22.--A DEAL IN EGGS.
A man went recently into a dairyman's shop to buy eggs. He wanted them of various
qualities. The salesman had new-laid eggs at the high price of fivepence each, fresh eggs
at one penny each, eggs at a halfpenny each, and eggs for electioneering purposes at a
greatly reduced figure, but as there was no election on at the time the buyer had no use
for the last. However, he bought some of each of the three other kinds and obtained
exactly one hundred eggs for eight and fourpence. Now, as he brought away exactly the
same number of eggs of two of the three qualities, it is an interesting puzzle to determine
just how many he bought at each price.
23.--THE CHRISTMAS-BOXES.
Some years ago a man told me he had spent one hundred English silver coins in