To conceal the trick better, it will be sufficient to ask whether the sum of the two products can be halved without a remainder; for in that case the total will be even, and in the contrary case odd.
It may be readily seen, that the pieces, instead of being in the two hands of the same person, may be supposed to be in the hands of two persons, one of whom has the even number, or piece of gold, and the other the odd number, or piece of silver. The same operations may then be performed in regard to these two persons, as are performed in regard to the two hands of the same person, calling the one privately the right and the other the left.
THE NUMBER BAG
The plan is to let a person select several numbers out of a bag, and to tell him the number which shall exactly divide the sum of those he has chosen; provide a small bag, divided into two parts, into one of which put several tickets, numbered, 6, 9, 15, 36, 63, 120, 213, 309, etc.; and in the other part put as many other tickets marked number 3 only. Draw a handful of tickets from the first part, and, after showing them to the company, put them into the bag again, and, having opened it a second time, desire any one to take out as many tickets as he thinks proper; when he has done that, you open privately the other part of the bag, and tell him to take out of it one ticket only. You may safely pronounce that the ticket shall contain the number by which the amount of the other numbers is divisible; for, as each of these numbers can be multiplied by 3, their sum total must, evidently, be divisible by that number. An ingenious mind may easily diversify this exercise, by marking the tickets in one part of the bag with any numbers that are divisible by 9 only, the properties of both 9 and 3 being the same; and it should never be exhibited to the same company twice without being varied.
THE MYSTICAL NUMBER NINE
The discovery of remarkable properties of the number 9 was accidentally made, more than forty years since, though, we believe, it is not generally known.
The component figures of the product made by the multiplication of every digit into the number 9, when added together, make Nine.
The order of these component figures is reversed after the said number has been multiplied by 5.
The component figures of the amount of the multipliers (viz. 45), when added together, make Nine.
The amount of the several products or multiples of 9 (viz. 405), when divided by 9, gives far a quotient, 45; that is, 4 plus 5 = Nine.