Such numbers must be offered as are divisible by 9; such, for instance, as 36, 63, 81, 117, 126, 162, 207, 216, 252, 261, 306, 315, 360, and 432.
Then let a person choose any two of these numbers, and after adding them together in his mind, strike out any one of the figures he pleases, from the sum.
After he has done this, desire him to tell you the sum of the remaining figures; and that number which you are obliged to add to this amount, in order to make it 9, or 18, is the one he struck out.
For example, suppose he chose the numbers 126 and 252, the sum of which is 378.
Then, if he strike out 7 from this amount, the remaining figures, 3 and 8, will make 11; to which 7 must be added to make 18.
If he strike out the 3, the sum of the remaining figures, 7 and 8, will be 15; to which 3 must be added, to make 18; and so in like manner, for the 8.
By knowing the last Figure of the Product of two Numbers, to tell the other Figures.
If the number 73 be multiplied by each of the numbers in the following arithmetical progression, 3, 6, 9, 12, 15, 18, 21. 24, 27, the products will terminate with the nine digits, in this order, 9, 8, 7, 6, 5, 4, 3, 2, 1; the numbers themselves being as follows, 219, 438, 657, 876, 1095, 1314, 1533, 1752, and 1971.
Let therefore a little bag be provided, consisting of two partitions, into one of which put several tickets, marked with the number 73; and into the other part, as many tickets numbered 3, 6, 9, 12, 15, 18, 21, 24, and 27.
Then open that part of the bag which contains the number 73, and desire a person to take out one ticket only; after which, dexterously change the opening, and desire another person to take a ticket from the other part.