Part 17

Supposing the River Murray to be three cubits in breadth--which it isn’t--what is the average height of the Alps, stocks being at nineteen and a-half?

If in autumn apples cost fourpence per pound in Melbourne, and potatoes a shilling a score in spring, when will greengages be sold in Brisbane at three-halfpence each, Sydney oranges being at a discount of five per cent.?

If two men can kill twelve kangaroos in going up the right side of a rectangular turnip-field, how many would be killed by five men and a terrier pup in going down the other side?

If a milkmaid four feet ten inches in height, while sitting on a three-legged stool, took four pints of milk out of every fifteen cows, what was the size of the field in which the animals grazed, and what was the girl’s name, age, and the occupation of her grandfather?

If thirty thousand millions of human beings have lived since the beginning of the world, how many may we safely say will die before the end of it? N.B.--This example to be worked out by simple subtraction, algebra, and the rule of three. Compare results.

72. Find two numbers in the proportion of 9 to 7 such as the square of their sum shall be equal to the cube of their difference.

ARITHMETICAL THOUGHT READING.

A great deal of fun can be derived from puzzles of this nature--they are endless in variety--and as they depend upon some principle in arithmetic should be easily remembered.

Example 1. Think of a number, say 5 Double it 10 Add 5 15 Add 12 27 Take away 3 24 Halve it 12 Take away number first thought of--5 The answer will always be 7

Example 2. Think of a number, say 8 Square it 64 Subtract the square of the number which is 1 less than the number thought of--that is 7--whose square is 49--leaves 15 Add 1 16

When this last number is told, halve it, and you will arrive at the original number--8.

Example 3. Think of a number, say 9 Multiply by 3 27 Add 2 29 Multiply by 3 87 Add 2 more than the number thought of (11) 98

The number of tens in the last answer gives the number thought of, viz., 9.

Example 4. Think of a number, say 7 Multiply by 3 21 [If product be odd] add 1 22 Halve it 11 Multiply by 3 33 [If product be odd] add 1 34 Halve it 17

Ask how many 9’s are in the remainder, when, of course, the reply will be 1.

The secret is to bear in mind whether the first sum be odd or even. If odd first time, retain 1 in the memory; if odd a second time, 2 more, making 3; to which add 4 for every 9 contained in the remainder.

In the above example, there being only one 9 in 17, this gives us 4, which added to 3 produces the number thought of--7. When even simply add 4 for every 9 in remainder.

HOW TO TELL THE AGE OF A PERSON.

Tell a person to write down the figure which represents the day of the week on which he was born;--thus, 1 for Sunday, 2 for Monday, and so on; next, the figure for the month--1 for January, 2 for February, &c.; then the date of the month; now tell him to multiply the number thus formed by 2, add 5, multiply by 50, and then to add his age, and from this sum to subtract 365; now you ask him for the remainder, to which you secretly add 115.

The result will be:--The first figure, the day of the week; the next, the month in the year; the next, the date of the month; and the last, the age in years.

Example:

A person was born on Wednesday, 11th June, 1863.

Write 4, as Wednesday is 4th day of the week. " 6, as June is 6th month of year. " 11, as that is the date given, 11th June.

The figures then are-- 4611 2 ---- 9222 5 ---- 9227 50 ------ 461350 35 Age ------ 461385 365 ------ 461020 115 -------- 4-6-11-35

A GOOD FIGURE TRICK.

Tell a person to set down a sum of money less than £12, in which the pounds exceed the pence; next to reverse this amount, making pence pounds, etc., and to subtract the one from the other, then set beneath the result itself reversed, adding the last two lines together, when you will tell him the result, which will always be £12 18s. 11d.

Example: £10 8 7 7 8 10 -------- 2 19 9 9 19 2 -------- £12 18 11

If the performer be blindfolded the trick looks very mystifying; he should not, however, repeat it, for many would soon discover the secret, but as the peculiarity is not confined to money, other illustrations can be given if required--for instance--if a number of yds., ft. and inches (less than 12 yds.) be operated on, the final answer will always be 12 yds. 1 ft. 11 inches; and if a number of cwts., qrs. and lbs. (less than 28 cwts.) be chosen, the answer will always be 28 cwts. 2 qrs. 27 lbs.