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 first is | 8; | to which add | 2, | the sum is | 10 |
| The second is | 12; | subtract | 2, | the remainder is | 10 |
| The third is | 5; | multiplied by | 2, | the product is | 10 |
| The fourth 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. | |
| 8 + 6 + 4 + 1 + 9 + 7 + 5 + 3 + 2 = 45. |