Effect:
Three objects are placed in a row on the table, their positions designated
as 1, 2, 3. These numbers refer not to the objects, but to their positions.
The magician turns his back. The spectator now switches the position of
any two objects, calling out the numbers of the two positions. Thus if
he switches the object in the positions 1 and 3 he calls out the number
1 and 3. He continues switching pairs of objects as long as he wishes,
always calling out the number with each change.
When he tires of doing this, he pauses and thinks of any one of the three objects.
Then he switches the position of the other two
without telling the magician the positions involved in this switch.
After this is done, he goes back to switching pairs at random again, each time
calling out the positions being switched, and continues until he tires.
The magician turns around and immediately points out to the chosen object.
Method:
Described in 'Mathematics, Magic and Mytery'
(Martin Gardner 1956).
Training:
Here are the three objects.