Physical Amusements and Diverting Experiments / Composed and Performed in Different Capitals of Europe, and in London

CHAP. XIV.

A mathematical Combination for guessing, in a whole pack composed of fifty-two Cards, how many Points will make the Cards under each Parcel, which Parcels are to be made by one of the Company, observing to him that each Parcel he makes is to compose the Number of Thirteen, to begin from the Point of the first Card which he takes to form each Parcel.

EXAMPLE.

The pack having been shuffled by one or more persons, make it be cut by as many persons as you think proper.

Then desire one of the company to form the parcels of cards, all which must contain thirteen each, beginning by the first card he takes up.

Suppose that this first card is a nine, the next will be called ten, and so on till thirteen; consequently this first parcel will be composed of five cards	5
If the next card should be an ace, the ace counting only one, the next parcel will therefore be composed of thirteen cards	13
Suppose the next card is a court card, or a ten, they being of the same value, this parcel will contain, in order to make up thirteen, four cards	4
If the following should be a five, then the fourth parcel will contain nine cards	9
Should the next parcel be a seven, the fifth parcel will be composed of seven cards	7
A court card being the first of this parcel, it will be composed of four cards	4
If the seventh begins by an eight, it will be composed of six cards	6
In that case the eighth cannot be made, except it begins by a ten, or a court card, since there remains only four cards to employ the whole number of the cards, which is fifty two	4
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Sum total	52
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In the supposition then that this eighth parcel begins by a ten, or court card, which is the same, there would remain no cards, and you would have eight parcels.

If it began by any other card, not adapted to make out thirteen, there would remain four cards, which must be spread on the table, without discovering them.

In order to find out the number of points contained under each of the parcels, whether they be to the amount of eight, or only seven, and four cards remaining, you must make use of the following method:

Without touching the cards, separate in your mind four parcels; then multiply silently by 14 the remaining parcels, whether they are four or only three.

In the first case you are to say in your mind, 4 times 14 are 56, then add to this number one point for each of the parcels that you have separated in your mind, which will make 60. Then make the eight parcels be turned up, and count the number of points contained in each of the cards that are under, you will then find 60, observing that the aces count only for one point, and the court cards for 10.

If there should be only 7 parcels, you will have 4 cards remaining; you will however separate 4 in your mind; then you are to multiply the 3 remaining parcels by 14; and say to yourself, 3 times 14 is 42, and 4 for the 4 parcels that you separated, make 46; to which you must add 4 more for the 4 cards that will remain, which will make 50. On turning up the 7 parcels you will necessarily find 50.

If by chance each parcel should begin by an ace, which is possible, you could then make only 4 parcels, and as it must be the 4 aces, that would be found under, you would only have 4 points.

If it happened also, that three parcels began each by an ace, it would then take up 39 cards; it is probable that in such a case there would be only four parcels in all, and a few cards remaining: you must then content yourself with counting as many points as parcels; to which you will add one point for each of the remaining cards, and this will amount infallibly to the just number of the points of the cards under the four parcels.

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