As it is necessary that the cards presented should be distinguished, we
shall call the first A, the second B, and the third C. Let the persons,
whom we shall distinguish by first, second, and third, choose privately
whichever of the cards they think proper, and when they have made their
choice, which is susceptible of six variations, give the first person 12
counters, the second 24, and the third 36: then desire the first person
to add together the half of the counters of the person who has chosen
the card A; the third of those of the person who has chosen B; and the
fourth part of those of the person who has chosen C; and ask the sum,
which must be either 23 or 24, 25 or 27, 28 or 29, as in the following
table:
First. Second. Third. Sums.
12 24 36
A B C 23
A C B 24
B A C 25
C A B 27
B C A 28
C B A 29
This table shows, that if the sum is 25, for example, the first person
must have chosen the card B, the second the card A, and the third the
card C; and that, if it be 28, the first person must have chosen the
card B, the second the card C, and the third the card A; and so of the
rest.