SIXTEEN CARDS BEING IN TWO ROWS, TO FIND THAT WHICH A PERSON HAS THOUGHT OF.
The cards being arranged as follow, desire the person to think of one, and to observe well in which row it is:
| A | B | C | D | E | F | H | I |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | * |
| 0 | 0 | 0 | 0 | * | 0 | 0 | 0 |
| 0 | 0 | * | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| * | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Let us suppose that the card thought of is in the row A: take up the whole row in the order in which it now stands, and dispose it in two rows C and D, in such a manner, that the first card of the row A may be the first of the row C; the second of the row A, the first of the row D; and so on, transferring the 16 cards from A and B, to C and D. This being done, again ask in which of the vertical rows the card thought of stands. We shall suppose it to be in C; remove that row as well as D, observing the same method as before; and continue in this manner until the card thought of becomes the first of the row I. If you then ask in which row it is, it may be immediately known, because after the last operation it will be the first in the row said to contain it; and as each row has a distinguishing character or sign, you may cause them all to be mixed with each other, and still be able to discover it by the sign you have remarked.
If a greater number of cards be employed, disposed in two vertical rows, the card thought of will not be at the top of the row after the last transposition: if there are 33 cards, 4 transpositions will be necessary; if 64 there must be 5; and so on.