To guess, by smelling, which has been the Number struck out by a Person in the Company, in the Product of a Multiplication given him to do.

Propose to a person of the company to multiply, by whatever number he pleases, one of the three sums which you will give him on a piece of paper; desire him to strike out whatever figure he pleases of the product of his multiplication, let him change and invert the order of the remaining figures after the defalcation he has chosen.

While the person is making his calculation and the subsequent operations, go in another room: when you are told you may return, desire the person who has done the multiplication, to give you the remaining product on a piece of paper or card; put it to your nose as though you would smell it; then you will tell him, to the great astonishment of the whole Company, what figure he had struck out.

In order to do this operation, first observe, that the figures composing each of the three sums you propose to be multiplied, do not exceed the number of 18.

EXAMPLE.

Suppose the three sums proposed to be the following:

Suppose likewise that the figure which has been struck out is the 6, the remaining ones will form a sum of 92,478.

As you let the person who has done the multiplication set down the figures in the order he pleases, suppose also that he sets them down thus, on the piece of paper he gives you,

79,482.

When you pretend to smell the paper, add together in your mind the figures presented to you, in order to reduce them to nines; and say in your mind 7 and 2 make nine; after that 8 and 4 make 12; in 12 there is 9, and three remains towards 9 more; to complete which 6 is wanting, which is and must be the figure struck out. This calculation must be made quickly, and while you pass the paper under your nose under the pretext of smelling it.

There is another manner of proceeding to guess the figure left out, by letting the person chuse the sum he pleases to be multiplied, but then you must ask him to shew you the sum he means to have multiplied, and to let you add one figure at your option.

In that case, by running your eyes over the sum set down, you will easily see what figure you are obliged to add in order to complete the number of 9.

EXAMPLE.

In the supposition that the sum set down is the following:

789,788

Add in your mind thus: 7 and 8 are 15, and 9, 24; and 7, 31; and 8, 39; and 8 more, 47: in 47 there is 5 times 9, as 9 times 5 make 45; there remains 2, therefore in order to complete 9, 7 are to be added; consequently the sum to be multiplied will be 7,897,887.

Then give this sum, which has been increased by a 7, to the person who has presented it to you: and tell him to chuse whatever multiplier he pleases; then retire while he does the multiplication, recommending him to strike out the figure he pleases, as usual, and to set down on a piece of paper the remaining sum, the figure being defalcated, and the remaining figures ranged as he pleases; and in order to guess the number that was struck out, you are to proceed as it has been explained for the first manner of operating, and with the same tricks.