Hand a pack of cards to a party, requesting him to make up parcels of cards, in the following manner. He is to count the number of pips on the first card that turns up, say a five, and then add as many cards as are required to make up the number 12; in the case here supposed, having a five before him, he will place seven cards upon it, turning down the parcel. All the court cards count as 10 pips; consequently, only two cards will be placed on such to make up 12. The ace counts as only one pip.
He will then turn up another, count the pips upon it, adding cards as before to make up the number 12; and so on, until no more such parcels can be made, the remainder, if any, to be set aside, all being turned down.
During this operation, the performer of the trick may be out of the room, at any rate, at such a distance that it will be impossible for him to see the first cards of the parcels which have been turned down; and yet he is able to announce the number of pips made up by all the first cards laid down, provided he is only informed of the number of parcels made up and the number of the remainder, if any.
The secret is very simple. It consists merely in multiplying the number of parcels over four by 13 (or rather vice versa), and adding the remaining cards, if any, to the product.
Thus, there have just been made up seven packets, with five cards over. Deducting 4 from 7, 3 remain; and I say to myself 13 times 3 (or rather 3 times 13) are 39, and adding to this the five cards over, I at once declare the number of pips made up by the first cards turned down to be 44.
There is another way of performing this striking trick. Direct six parcels of cards to be made up in the manner aforesaid, and then, on being informed of the number of cards remaining over, add that number to 26, and the sum will be the number of pips made up by the first cards of the six parcels.
Such are the methods prescribed for performing this trick; but I have discovered another, which although, perhaps, a little more complicated, has the desirable advantage of explaining the seeming mystery.
Find the number of cards in the parcels, by subtracting the remainder, if any, from 52. Subtract the number of pip cards therefrom, deduct this last from the number made up of the number of parcels multiplied by 12, and the remainder will be the number of pips on the first cards.
To demonstrate this take the case just given. There are seven parcels and five cards over. First, this proves that there are 47 cards in the seven parcels made up of pips and cards. Secondly, subtract the number of pip cards—seven from the number of cards in the parcels; then, 7 from 47, 40 remain (cards). Thirdly, now, as the seven parcels are made up both of the pip cards and cards, it is evident that we have only to find the number of cards got at as above, to get the number of pips required. Thus, there being seven packets, 7 times 12 make 84; take 40, as above found (the number of cards), and the remainder is 44, the number of pips as found by the first method explained,—the process being as follows:—
52 - 5 = 47 - 7 = 40.
Then, 7 X 12 = 84 - 40 = 44.