Amazing maze/Law of Squares
Meat Truck ( (no email) )
Sun, 27 Sep 1998 02:11:14 -0500
Hello all. I spent many hours on the following chess problem which yields
an amazing result when the solution is found. I would assume this is a
unique or solitary solution. Start a chess knight at the corner of the
board and move it 63 times so that it has touched every square. This
implies that the knight cannot move to a spot that has been previously
occupied. Trying to solve this problem gets like a maze of travel that
leads to a dead end where the next move cannot be made because you've been
there before. The best I was able to do was to leave 4 unoccupied spaces
on the board before becoming trapped. When the correct 64 numbered sequence
is found and each square is given a number on the board it is observed that
all the rows and columns add to the same number. But the diagonals do not
add to this number which means that it is not a perfect magic square. I
was wondering if anyone out there could easily figure the odds on randomly
selecting this supposed unique solution, (which could also be shown 8
ways).
Speaking of odds and magic squares the following facts might seem
amazing. Given a magic square of 100 numbers, how many different unique
solutions could there be? Once the method of construction is learned it is
readily evident that over 37,000 trillion,(yes 3.7 times 10 the 16th power)
possible arrangements of numbers can satisfy the condition of being a magic
square of one hundred numbers. Perhaps more amazing than this is that when
Searl first shows a square of 100 numbers in book 1 of the Law of Squares
he does not use one these easily readily shown solutions but rather uses
tricks to derive a different solution in which if all the tricks were
included the true odds become mind numbing or confusing to say the least.
Three books and $150 dollars later we find at the end of book 2 a corrected
square sent in by John Thomas,his American supporter and dealer of Searls
books. To this Searl responds "yes I did dropped a clanger thanks John for
pointing it out" (the professor doesnt bother too much with spelling or
literary context). So okay everyone can make a mistake. But Two? The first
square of significance in learning the construction of these squares is the
eight square of 64 numbers. This can be shown to have 331,176 readily
evident possibilities (according to what I deduced,not Searl) But does
Searl use one of these? No, only in this square he violates his own
construction laws but still produces a magic square which actually means a
third of a million possibilities is a conservative estimate. In short Searl
seems to want to make an explanation of construction of these squares a
most difficult endeavor which is most irritating to someone trying to
decipher the method. Again at the back of book 2 Thomas sends this message.
"In doing the squares I noticed that square 8 was not symmetrical. I have
enclosed a "corrected" square 8 and would like to know if it is correct
according to your law of squares." Also a corrected square 12 is submitted
by John Thomas. Searl also notes at the finish of these submissions "Most
of the mistakes are there on purpose to check if you are studying these
books or not." Well I studied the first 4 of these but the only way I was
able to know that I had an understanding of what was going on was to
construct the squares for myself. Since I was incarcerated for 4 months for
traveling without a liscense I had time for these considerations, and
plenty of chess games too. This kind of astounded inmates when I produced a
magic square of 144 numbers and we weren't allowed to possess a
calculator! Now if Searl had used a correct magic square of 64 numbers he
could have left the following puzzle for everyones enjoyment, but he didnt
and so I will. A uniform square consists of the numbers 1-64 in sequence in
rows or columns. Construct a balanced or magic square in which only half of
these numbers are allowed to be moved from their uniform position.
Sincerly rebounding from past and current misfortune; Harvey D. Norris
mnorris@akron.infi.net
PS: To possibly glimpse where all of this led me visit my message board at
www.insidetheweb.com/mbs.cgi/mb124201 or email me directly if interested in
Searl book exchange.