Arithmetic is the fundamental branch of mathematics dealing with numbers and the basic operations: addition, subtraction, multiplication, and division. Questions involve performing these operations, understanding number properties (like integers, fractions, decimals), and solving related word problems.
A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish; but they were only to continue the gift so long as they could make it in different ways, always giving eighteenpence each to a number of women and half a crown each to men. During how many years could the charity be administered? Of course, by "different ways" is meant a different number of men and women every time.
"Whom do you think I met in town last week, Brother William?" said Uncle Benjamin. "That old skinflint Jorkins. His family had been taking him around buying Christmas presents. He said to me, 'Why cannot the government abolish Christmas, and make the giving of presents punishable by law? I came out this morning with a certain amount of money in my pocket, and I find I have spent just half of it. In fact, if you will believe me, I take home just as many shillings as I had pounds, and half as many pounds as I had shillings. It is monstrous!'" Can you say exactly how much money Jorkins had spent on those presents?
It will be found that £`66, 6`s. `6`d. equals `15,918` pence. Now, the four `6`'s added together make `24`, and the figures in `15,918` also add to `24`. It is a curious fact that there is only one other sum of money, in pounds, shillings, and pence (all similarly repetitions of one figure), of which the digits shall add up the same as the digits of the amount in pence. What is the other sum of money?
The largest sum of money that can be written in pounds, shillings, pence, and farthings, using each of the nine digits once and only once, is £`98,765, 4`s. `3`½d. Now, try to discover the smallest sum of money that can be written down under precisely the same conditions. There must be some value given for each denomination—pounds, shillings, pence, and farthings—and the nought may not be used. It requires just a little judgment and thought.
What is the largest sum of money—all in current silver coins and no four-shilling piece—that I could have in my pocket without being able to give change for a half-sovereign?
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 `2`s. more in his box than at present, if William had had `2`s. 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 `45`s., 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.
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—`2`s. `2`½d. 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.
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.
Some years ago a man told me he had spent one hundred English silver coins in Christmas-boxes, giving every person the same amount, and it cost him exactly £`1, 10`s. `1`d. Can you tell just how many persons received the present, and how he could have managed the distribution? That odd penny looks queer, but it is all right.