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The Gaming Table by Andrew Steinmetz, Volume II

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Amusing Card Tricks

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.

In general, however, the first method, being the easiest of
performance, should be adopted. The second is in many respects
very objectionable.

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