
SOMA News 
27 Jan 2000
EMail. 
!! ChunJu Lai's proof has been disputed by Bob Nungester,
Read his comments at the end of this letter. 
I just received a short mail from Taiwan, Including a
nice and simple proof that the WWall is still
impossible.
Although structurally different, it actually resembles
the original "Jotun's Proof", as it was made by Jotun
Piet Hein.
Jotun's proof is working from the basis of checkerboarding
a figure. (Described on page 38 of the Parker brothers
manual [Newsletter 1998.12.10])
To see another description of checkerboarding, enter the
main SOMA page, go to the SOLVER section, and then select
SOLVER MANUAL. Here click on "How did we speed it extra up".
This proof is by: ChunJu Lai (13 years old) junior high
grade 1 student, and member of the "Chiu Chang Math. Club."
The words "Chiu Chang" means "Nine Chapters", in reference to an ancient Chinese scroll on mathematics. ChunJu Lai lives in HsinChu (70 KM far from Taipei, Taiwan). < ChunJu Lai with some of his SOMA cubes 
If we color the columns of the 'WWall' in an alternating fashion,
starting by coloring the first column black.
The total will be 15 black to 12 white.
Now, we examine each of the seven SOMA pieces, testing each in
all possible orientations to ascertain the maximum number of
black cubes it can have.
Because the pieces #5,#6,#7 are two levels in any direction, they
must placed in a corner of the figure, except in first and last
columns.
So, #5 must 1 black 3 white ;
#6 must 1 black 3 white ;
#7 must 2 black 2 white.
The remaining pieces are: then
#1 #2 #3 #4 #5 #6 #7 Black 2(Max) 3(Max) 3(Max) 2 1 1 2 White 1(Min) 1(Min) 1(Min) 2 3 3 2
This chart show that the maximum number of black is 14,
NOT enough for Figure A033, which is thus impossible.
PS: The Math club is based in, Chiu Chang Math. Books & Puzzles Co.
which owned by mr. WenHsien SUN. and located at.
7Fl,No.51,Alley 15,Lane 147,Sec.3,ShinYi Road
Taipei,Taiwan,R.O.C.
TEL:886227048405
FAX:886227067353
ccmp@tpts1.seed.net.tw
http://www.hk.super.net/~phcheung/ccmp.html
The compagny publishes only good books in mathematics, and
imports meaningful mathematical games and puzzles into Taiwan.
DISPUTE:
ChunJu Lai's proof has been disputed by Bob Nungester
bnungest@tycoelectronics.com
In this letter of 10. mar. 2000 where Bob writes:
I'm always interested in new ways to solve Soma figures,
so I read ChunJu Lai's proof for the WWall to see if there
was anything new.
The idea of identifying corners is interesting, but in
analyzing the proof I don't think this particular argument
works.
Pieces 5 and 6 do have to go in the corners, but they can
be placed in a corner and have two black cubes and two
white cubes (not 1 black, 3 white).
If you look at the orientation of piece 1 in his diagram
and attach a fourth cube to the top cube in order to make
piece 5 or 6, you will get an orientation with 2 black,
2 white which could be put in a corner.
Coloring the cubes this way, is another form of parity.
we often refer to as Parity II.