If a hundred stones be placed in a straight line, at the distance of a yard from each other, the first being at the same distance from a basket, how many yards must the person walk who engages to pick them up, one by one, and put them into the basket? It is evident that, to pick up the first stone, and put it into the basket, the person must walk two yards; for the second, he must walk four; for the third, six: and so on increasing by two, to the hundredth.
The number of yards, therefore, which the person must walk will be equal to the sum of the progression, 2, 4, 6, &c., the last term of which is 200 (22). But the sum of the progression is equal to 202, the sum of the two extremes, multiplied by 50, or half the number of terms: that is to say, 10,100 yards, which makes more than 51⁄2 miles.
THE FAMOUS FORTY-FIVE.
How can number 45 be divided into four such parts that, if to the first part you add 2, from the second part you subtract 2, the third part you multiply by 2, and the fourth part you divide by 2, the sum of the addition, the remainder of the subtraction, the product of the multiplication, and the quotient of the division be all equal?
| The 1st is | 8; | to which add | 2, | the sum is | 10 |
| The 2nd is | 12; | subtract | 2, | the remainder is | 10 |
| The 3rd is | 5; | multiplied by | 2, | the product is | 10 |
| The 4th is | 20; | divided by | 2, | the quotient is | 10 |
| 45 |
Required to subtract 45 from 45, and leave 45 as a remainder?
Solution.— 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
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8 + 6 + 4 + 1 + 9 + 7 + 5 + 3 + 2 = 45
SUBTRACTION.
From 1 mile subtract 7 furlongs, 39 rods, 5 yards, 1 foot, 5 inches.