Mathematical_Recreations-Kraitchik-2e

Numerical Pastimes 89
3. CHINESE RINGS. The Chinese rings are a toy, consisting
of a fixed number of rings (usually from 5 to 8) hung
on a bar in such a way that the ring at the right end may be
taken off or put on the bar at pleasure, but any other can be
taken off or put on only when the next one to its right is on
FIGURE 12.
Chinese Rings.
and all the others to its right are off. The order of the rings
is fixed. Only one ring can be taken off or put on at a time,
except that the two rings at the extreme right can be put on
or taken off together. When we operate with these rings
separately we shall say that we work the slow way; when the
(1) * * * * * * *
(2) * * * * * * 0
(3) * * * * * 0 *
(4) * * * * * 0 0
(5) * * * 0 * 0 0
FIGURE 13. Taking Chinese Rings off the Bar; the * Indicates
a Ring on the Bar, 0 a Ring off.
two are put on or taken off together, we shall say we work
the fast way.
Let us denote the position of the rings by a set of asterisks
(*) and zeros (0) in order, * if the ring is on the bar, 0 if it is
off. In the accompanying figure, for a toy with 7 rings, position
(1) indicates that all rings are on the bar. We can pass
from position (1) to position (2) or to position (3) in one step,