You may then pronounce, that this ticket shall contain the number by which the amount of the other numbers is divisible; for, as each of these numbers is some multiple of 3, their sum must evidently be divisible by that number.
This recreation may also be diversified, by marking the tickets in one part of the bag with any numbers which are divisible by 9, and those in the other part of the bag with the number 9 only; the properties of both 9 and 3 being the same; or if the numbers in one part of the bag be divisible by 9, the other part of the bag may contain tickets marked both with 9 and 3, as every number divisible by 9 is also divisible by 3.
To find the Difference between any two Numbers, the greater of which is unknown.
Take as many 9’s as there are figures in the less number, and subtract the one from the other.
Let another person add that difference to the larger number; and then, if he take away the first figure of the amount, and add it to the remaining figures, the sum will be the difference of the two numbers, as was required.
Suppose, for example, that Matthew, who is 22 years of age, tells Henry, who is older, that he can discover the difference of their ages.
He privately deducts 22, his own age, from 99, and the difference, which is 77, he tells Henry to add to his age, and to take away the first figure from the amount.
Then if this figure, so taken away, be added to the remaining ones, the sum will be the difference of their ages; as, for instance:
| The difference between Matthew’s age and 99, is | 77 | |
| To which Henry adding his age | 35 | |
| The sum will be | 112 | |
| And 1, taken from 112, gives | 12 | |
| Which being increased by | 1 | |
| Gives the difference of the two ages | 13 | |
| And, this added to Matthew’s age | 22 | |
| Gives the age of Henry, which is | 35 |
A Person striking a Figure out of the Sum of two given Numbers, to tell him what that Figure was.