I am looking for someone who can either confirm or deny first-hand the
" In China there exists a game called 'tsyan-shidzi', which means
'choosing stones'. The game is for two players, and it goes as
follows: There are two piles of stones of arbitrary size. On each
turn, a player either removes from one pile an arbitrary number of
stones, or removes from both piles the same number of stones. The
player who takes the last stone wins. "
The above claim is often made in connection with Wythoff's game.
Wythoff invented his game in 1907, and it is essentially the game
When people describe Wythoff's game and its mathematical analysis,
they often remark that the game already existed in China under the
name of 'tsyan-shidzi', as mentioned above. The claim is made, for
example, by Martin Gardner in "Penrose Tiles to Trapdoor Ciphers"
(Freeman, 1989), in the chapter on Wythoff's Nim. It is also made by
Yaglom and Yaglom, in "Challenging Mathematical Problems with
Elementary Solutions, Vol 2" (Holden-Day, 1967), (page 20, I think). I
am not sure what is the original source for the claim.
My academic advisor, however, has some reservations on this. He has
asked several Chinese people, and no one could even confirm that
'tsyan-shidzi' belongs to the Chinese language! Sometimes stories
about faraway lands pop up on their own...
Therefore, I was wondering whether someone could confirm first-hand
whether 'tsyan-shidzi' (or something similar) means "choosing stones"
in Chinese, and whether the above game existed in China, maybe as some
sort of a childish game or something like that.
Thanks in advance.
Request for Question Clarification by
23 Jul 2004 21:08 PDT
I have spoken with a friend from mainland China, a PhD mathematician
who is very interested in recreational mathematics and also a strong
Go (Weichi) tournament player. He too doesn't believe there is any
game like Nim widely known in China; he says his own introduction to
Nim was reading Knuth.
There seem to be two independent sources of a Chinese attribution for
the game, one from an American writer Bouton, generally credited with
having published the first analysis of Nim and with giving it that
It is reported that he later retracted his published claim (circa
1902) that Nim was similar to a Chinese game Fan-Tan.
More recently than that, but earlier than the sources you cited, I've
located a source for the specific "tsyan-shidzi" term. I'm having a
"go" (pun intended) at tracking down a physical copy of this work to
see if it sheds any light on the claim.
My thought is to post a note from my Chinese friend about this
passage, and to provide you with as much information as can be
obtained from that work.
As the terms Go (Japanese) and Weichi (Chinese) illustrate, there can
be quite different traditional names for unmistakably the same game.
However my friends lack of awareness of a game like Nim in China is
(for me) pretty telling.
On the other hand, despite growing up in a major city of the Szechuan
province of China, he'd never heard of hot and sour soup before coming
to America. Just shows that travel can broaden ones perspectives!
Request for Question Clarification by
27 Jul 2004 20:33 PDT
Well, my request to my Chinese friend was answered this way:
I can translate the strange spelling of the Chinese
TSYANSHIDZI; it means "pick stones". However it doesn't
reflect any game that I played in Childhood.
On the other hand, many interesting Chinese games have
originated from Tibet (rumor has it that Go originated
from Tibet, too). There may be some version of it that
existed in Tibet or Mongolia or something.
I can be 99.99% sure if you ask an ordinary Chinese person,
s/he will not know what this game is about.
My request to Russian colleagues for an original of this translated work:
Domoryad, A.P. Mathematical Games and Pastimes
(Elmsford, NY: Pergamon Press, 1963)
has not yet met with success.
Clarification of Question by
28 Jul 2004 07:19 PDT
So "tsyanshidzi" does mean something like "choosing stones", after
all. That gives more credibility to the claim, I think. Of course, the
fact that most Chinese people haven't heard about this game doesn't
mean that the claim is necessarily false. The game might have existed
some isolated rural area, or something.
Can you ask your friend what he meant by "strange spelling"? What
would be the standard way of spelling it? Excuse my ignorance of
I got the English version of that Russian title from my library. It
refers to the game as:
the Chinese national game tsyanshidzi ("picking stones").
It gives two references to the game. Interestingly, one of them is
apparently the Russian original of the title by Yaglom and Yaglom that
I mentioned previously. So apparently Yaglom and Yaglom is an earlier
reference than Domoryad.
The second reference given is:
Uspenskii, Y. (1924) "Selected Mathematical Pastimes", pp. 43--52.
which is also probably a Russian title. I don't know if there is any
reference to tsyan-shidzi there, though.
Tell me what else you find. Could you check out that title by Uspenskii?