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“ It will 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.”
Note 4. p. 79.
It is by discovering the number of counters left on the board that this trick is performed. By means of a table the problem may be immediately solved, but as such a reference would be inconvenient, and, indeed, destructive to the magic of the trick, a Latin verse is substituted, which may be easily carried in the memory, and will be found to answer all the purposes of a table. In order, however, that the reader may become thoroughly ac. quainted with the machinery of the trick, we shall explain it in the words of its author. The problem is stated as follows: “ Three things being privately distributed to three persons, to guess that which each has got.”
Let the three things be a ring, a shilling, and a glove. Call the ring A, the shilling E, and the glove 1; and in your own mind distinguish the persons by calling them first, second, and third. Then take twenty-four counters, and give one of them to the first person, two to the second, and three to the third. Place the remaining eighteen on the table, and then retire, that the three persons may distribute among themselves the three things proposed without your observing them. When the distribution has been made, desire the person who has the ring to take from the eighteen remaining counters as many as he has already; the one who has the shilling to take twice as many as he has already, and the person who has the glove to take four times as many; according to the above supposition then, the first person has taken one, the second four, and the third twelve; consequently, one counter only remains on the table. When this is done, you may return, and by the number left, can discover what thing each person has taken, by employing the following words :
To make use of these words, you must recollect, that in all cases there can remain only 1, 2, 3, 5, 6, or 7 counters, and never 4. It must likewise be observed, that each syllable contains one of the vowels, which we have made to represent the things proposed, and that the first syllable of each word must be considered as representing the first person, and the second syllable the second. This being comprehended, if there remains only one counter, you must employ the first word, or rather the two first syllables, sal-ve, the first of which, that containing a, shows that the first person has the ring represented by A; and the second syllable, that containing E, shows that the second person has the shilling represented
by E; from which you may easily conclude that the third person has the glove. If two counters should remain, you must take the second word cer-ta, the first syllable of which, containing E, will show that the first person has the shilling represented by E ; and the second syllable containing A, will indicate that the second person has the ring, represented by A. In general, whatever number of counters remain, that word of the verse, which is pointed out by the same number must be employed.
Instead of the above Latin verse, the following French one might be used :
1 2 3 5
In using the above line, it must be considered as consisting only of six words.
This problem might be proposed in a manner somewhat different, and might be applied to more than three persons. Those of our readers who may be desirous of further information on the subject, must consult Bachet in the 25th of his Problèmes plaisantes et délectables.
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