[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.